What is the Greatest Common Factor of 39744 and 39752?

Greatest common factor (GCF) of 39744 and 39752 is 8.

GCF(39744,39752) = 8

We will now calculate the prime factors of 39744 and 39752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39744 and 39752.

How to find the GCF of 39744 and 39752?

We will first find the prime factorization of 39744 and 39752. After we will calculate the factors of 39744 and 39752 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 39752

Prime factors of 39752 are 2, 4969. Prime factorization of 39752 in exponential form is:

39752 = 2³ × 4969¹

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 39752

List of positive integer factors of 39752 that divides 39744 without a remainder.

1, 2, 4, 8, 4969, 9938, 19876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39744 and 39752. The biggest common factor number is the GCF number.
So the greatest common factor 39744 and 39752 is 8.

Also check out the Least Common Multiple of 39744 and 39752