What is the Greatest Common Factor of 39730 and 39744?

Greatest common factor (GCF) of 39730 and 39744 is 2.

GCF(39730,39744) = 2

We will now calculate the prime factors of 39730 and 39744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39730 and 39744.

How to find the GCF of 39730 and 39744?

We will first find the prime factorization of 39730 and 39744. After we will calculate the factors of 39730 and 39744 and find the biggest common factor number .

Step-1: Prime Factorization of 39730

Prime factors of 39730 are 2, 5, 29, 137. Prime factorization of 39730 in exponential form is:

39730 = 2¹ × 5¹ × 29¹ × 137¹

Step-2: 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-3: Factors of 39730

List of positive integer factors of 39730 that divides 39730 without a remainder.

1, 2, 5, 10, 29, 58, 137, 145, 274, 290, 685, 1370, 3973, 7946, 19865

Step-4: Factors of 39744

List of positive integer factors of 39744 that divides 39730 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39730 and 39744. The biggest common factor number is the GCF number.
So the greatest common factor 39730 and 39744 is 2.

Also check out the Least Common Multiple of 39730 and 39744