What is the Greatest Common Factor of 39744 and 39756?

Greatest common factor (GCF) of 39744 and 39756 is 12.

GCF(39744,39756) = 12

We will now calculate the prime factors of 39744 and 39756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39744 and 39756.

How to find the GCF of 39744 and 39756?

We will first find the prime factorization of 39744 and 39756. After we will calculate the factors of 39744 and 39756 and find the biggest common factor number .

Step-1: Prime Factorization of 39744

Prime factors of 39744 are 2, 3, 23. Prime factorization of 39744 in exponential form is:

39744 = 2⁶ × 3³ × 23¹

Step-2: Prime Factorization of 39756

Prime factors of 39756 are 2, 3, 3313. Prime factorization of 39756 in exponential form is:

39756 = 2² × 3¹ × 3313¹

Step-3: Factors of 39744

List of positive integer factors of 39744 that divides 39744 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46, 48, 54, 64, 69, 72, 92, 96, 108, 138, 144, 184, 192, 207, 216, 276, 288, 368, 414, 432, 552, 576, 621, 736, 828, 864, 1104, 1242, 1472, 1656, 1728, 2208, 2484, 3312, 4416, 4968, 6624, 9936, 13248, 19872

Step-4: Factors of 39756

List of positive integer factors of 39756 that divides 39744 without a remainder.

1, 2, 3, 4, 6, 12, 3313, 6626, 9939, 13252, 19878

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39744 and 39756. The biggest common factor number is the GCF number.
So the greatest common factor 39744 and 39756 is 12.

Also check out the Least Common Multiple of 39744 and 39756