What is the Greatest Common Factor of 31264 and 31280?

Greatest common factor (GCF) of 31264 and 31280 is 16.

GCF(31264,31280) = 16

We will now calculate the prime factors of 31264 and 31280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31264 and 31280.

How to find the GCF of 31264 and 31280?

We will first find the prime factorization of 31264 and 31280. After we will calculate the factors of 31264 and 31280 and find the biggest common factor number .

Step-1: Prime Factorization of 31264

Prime factors of 31264 are 2, 977. Prime factorization of 31264 in exponential form is:

31264 = 2⁵ × 977¹

Step-2: Prime Factorization of 31280

Prime factors of 31280 are 2, 5, 17, 23. Prime factorization of 31280 in exponential form is:

31280 = 2⁴ × 5¹ × 17¹ × 23¹

Step-3: Factors of 31264

List of positive integer factors of 31264 that divides 31264 without a remainder.

1, 2, 4, 8, 16, 32, 977, 1954, 3908, 7816, 15632

Step-4: Factors of 31280

List of positive integer factors of 31280 that divides 31264 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 23, 34, 40, 46, 68, 80, 85, 92, 115, 136, 170, 184, 230, 272, 340, 368, 391, 460, 680, 782, 920, 1360, 1564, 1840, 1955, 3128, 3910, 6256, 7820, 15640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31264 and 31280. The biggest common factor number is the GCF number.
So the greatest common factor 31264 and 31280 is 16.

Also check out the Least Common Multiple of 31264 and 31280