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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-03-21</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>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>First BanCorp Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-03-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>85027</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.41</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>672754</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Issued pursuant to the First BanCorp Omnibus Incentive Plan, as amended. The shares shall fully vest solely on the basis of the passage of time over a two year period on March 21, 2019. Notwithstanding vesting, the reporting person will be restricted from transferring the shares pursuant to additional TARP related restrictions.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Orlando Berges</signatureName>
        <signatureDate>2017-03-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
