<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-05-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001057706</issuerCik>
        <issuerName>FIRST BANCORP /PR/</issuerName>
        <issuerTradingSymbol>FBP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001464458</rptOwnerCik>
            <rptOwnerName>Berges Gonzalez Orlando</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P.O. BOX 9146</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN JUAN</rptOwnerCity>
            <rptOwnerState>PR</rptOwnerState>
            <rptOwnerZipCode>00908-0146</rptOwnerZipCode>
            <rptOwnerStateDescription>PUERTO RICO</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP and CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>First BanCorp Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2274</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.75</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>629705</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>First BanCorp Common Stock</value>
            </securityTitle>
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            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                    <value>728</value>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <value>628977</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
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                </directOrIndirectOwnership>
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            <securityTitle>
                <value>First BanCorp Common Stock</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>264990</value>
                    <footnoteId id="F2"/>
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                <transactionPricePerShare>
                    <value>0.00</value>
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                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>363987</value>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>First BanCorp Common Stock</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
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            </transactionTimeliness>
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                    <value>6629</value>
                    <footnoteId id="F3"/>
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                <transactionPricePerShare>
                    <value>5.75</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>357358</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>First BanCorp Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5306</value>
                    <footnoteId id="F4"/>
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                <transactionPricePerShare>
                    <value>5.75</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>352052</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>First BanCorp Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6734</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.75</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>345318</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>First BanCorp Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4878</value>
                    <footnoteId id="F6"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.75</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>340440</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Salary stock issued bi-weekly as a portion of the reporting person's salary compensation under the First BanCorp Omnibus Incentive Plan, as amended. Salary stock is fully vested on the date of grant. The number of shares represented by this award was determined by dividing the dollar value of the award granted to the reporting person by $5.75 (the closing price of the Issuer's common stock as quoted on the NYSE on May 10, 2017, the last trading day of the pay period). The shares reported as disposed of were withheld for taxes.</footnote>
        <footnote id="F2">Reflects the forfeiture of restricted stock resulting from the sale by the United States Department of the Treasury (&quot;U.S. Treasury&quot;) of its remaining shares of the Issuer's Common Stock at a price that, together with its proceeds from prior sales of the Issuer's Common Stock, resulted in its failure to recoup its entire original investment in the Issuer through the U.S. Treasury  Troubled Asset Relief Program Capital Purchase Program.</footnote>
        <footnote id="F3">Shares withheld to cover taxes related to restricted stock that vested pursuant to the terms of the restricted stock award dated March 21, 2012 but remained subject to TARP restrictions on transfer until the U.S. Treasury confirmed on May 10, 2017 that it had agreed to sell all of its remaining 10,291,553 shares of the Issuer's common stock, which caused that the restrictions on an additional 25% of the shares awarded were released as of such date.</footnote>
        <footnote id="F4">Shares withheld to cover taxes related to restricted stock that vested pursuant to the terms of the restricted stock award dated April 3, 2013 but remained subject to TARP restrictions on transfer until the U.S. Treasury confirmed on May 10, 2017 that it had agreed to sell all of its remaining 10,291,553 shares of the Issuer's common stock, which caused that the restrictions on an additional 25% of the shares awarded were released as of such date.</footnote>
        <footnote id="F5">Shares withheld to cover taxes related to restricted stock that vested pursuant to the terms of the restricted stock award dated March 27, 2014 but remained subject to TARP restrictions on transfer until the U.S. Treasury confirmed on May 10, 2017 that it had agreed to sell all of its remaining 10,291,553 shares of the Issuer's common stock, which caused that the restrictions on an additional 25% of the shares awarded were released as of such date.</footnote>
        <footnote id="F6">Shares withheld to cover taxes related to restricted stock that vested pursuant to the terms of the restricted stock award dated March 20, 2015 but remained subject to TARP restrictions on transfer until the U.S. Treasury confirmed on May 10, 2017 that it had agreed to sell all of its remaining 10,291,553 shares of the Issuer's common stock, which caused that the restrictions on an additional 25% of the shares awarded were released as of such date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Orlando Berges</signatureName>
        <signatureDate>2017-05-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
