What is the Greatest Common Factor of 39744 and 39748?

Greatest common factor (GCF) of 39744 and 39748 is 4.

GCF(39744,39748) = 4

We will now calculate the prime factors of 39744 and 39748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39744 and 39748.

How to find the GCF of 39744 and 39748?

We will first find the prime factorization of 39744 and 39748. After we will calculate the factors of 39744 and 39748 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 39748

Prime factors of 39748 are 2, 19, 523. Prime factorization of 39748 in exponential form is:

39748 = 2² × 19¹ × 523¹

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 39748

List of positive integer factors of 39748 that divides 39744 without a remainder.

1, 2, 4, 19, 38, 76, 523, 1046, 2092, 9937, 19874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39744 and 39748. The biggest common factor number is the GCF number.
So the greatest common factor 39744 and 39748 is 4.

Also check out the Least Common Multiple of 39744 and 39748