What is the Greatest Common Factor of 39680 and 39696?

Greatest common factor (GCF) of 39680 and 39696 is 16.

GCF(39680,39696) = 16

We will now calculate the prime factors of 39680 and 39696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39680 and 39696.

How to find the GCF of 39680 and 39696?

We will first find the prime factorization of 39680 and 39696. After we will calculate the factors of 39680 and 39696 and find the biggest common factor number .

Step-1: Prime Factorization of 39680

Prime factors of 39680 are 2, 5, 31. Prime factorization of 39680 in exponential form is:

39680 = 2⁸ × 5¹ × 31¹

Step-2: Prime Factorization of 39696

Prime factors of 39696 are 2, 3, 827. Prime factorization of 39696 in exponential form is:

39696 = 2⁴ × 3¹ × 827¹

Step-3: Factors of 39680

List of positive integer factors of 39680 that divides 39680 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 31, 32, 40, 62, 64, 80, 124, 128, 155, 160, 248, 256, 310, 320, 496, 620, 640, 992, 1240, 1280, 1984, 2480, 3968, 4960, 7936, 9920, 19840

Step-4: Factors of 39696

List of positive integer factors of 39696 that divides 39680 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 827, 1654, 2481, 3308, 4962, 6616, 9924, 13232, 19848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39680 and 39696. The biggest common factor number is the GCF number.
So the greatest common factor 39680 and 39696 is 16.

Also check out the Least Common Multiple of 39680 and 39696