What is the Greatest Common Factor of 39744 and 39762?

Greatest common factor (GCF) of 39744 and 39762 is 18.

GCF(39744,39762) = 18

We will now calculate the prime factors of 39744 and 39762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39744 and 39762.

How to find the GCF of 39744 and 39762?

We will first find the prime factorization of 39744 and 39762. After we will calculate the factors of 39744 and 39762 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 39762

Prime factors of 39762 are 2, 3, 47. Prime factorization of 39762 in exponential form is:

39762 = 2¹ × 3² × 47²

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 39762

List of positive integer factors of 39762 that divides 39744 without a remainder.

1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 2209, 4418, 6627, 13254, 19881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39744 and 39762. The biggest common factor number is the GCF number.
So the greatest common factor 39744 and 39762 is 18.

Also check out the Least Common Multiple of 39744 and 39762