Federal Home Loan Mortgage (FMCC) 10-Q 2012 Q2 Quarterly report

Exhibit 32.1

CERTIFICATION

PURSUANT TO 18 U.S.C. SECTION 1350,

AS ENACTED BY SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q for the quarter ended June 30, 2012 of the Federal Home Loan Mortgage Corporation (the “Company”), as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Donald H. Layton, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: August 7, 2012

/s/ Donald H. Layton

Donald H. Layton

Chief Executive Officer