What is the Greatest Common Factor of 39664 and 39680?

Greatest common factor (GCF) of 39664 and 39680 is 16.

GCF(39664,39680) = 16

We will now calculate the prime factors of 39664 and 39680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39664 and 39680.

How to find the GCF of 39664 and 39680?

We will first find the prime factorization of 39664 and 39680. After we will calculate the factors of 39664 and 39680 and find the biggest common factor number .

Step-1: Prime Factorization of 39664

Prime factors of 39664 are 2, 37, 67. Prime factorization of 39664 in exponential form is:

39664 = 2⁴ × 37¹ × 67¹

Step-2: 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-3: Factors of 39664

List of positive integer factors of 39664 that divides 39664 without a remainder.

1, 2, 4, 8, 16, 37, 67, 74, 134, 148, 268, 296, 536, 592, 1072, 2479, 4958, 9916, 19832

Step-4: Factors of 39680

List of positive integer factors of 39680 that divides 39664 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39664 and 39680. The biggest common factor number is the GCF number.
So the greatest common factor 39664 and 39680 is 16.

Also check out the Least Common Multiple of 39664 and 39680