What is the Greatest Common Factor of 31248 and 31264?

Greatest common factor (GCF) of 31248 and 31264 is 16.

GCF(31248,31264) = 16

We will now calculate the prime factors of 31248 and 31264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31248 and 31264.

How to find the GCF of 31248 and 31264?

We will first find the prime factorization of 31248 and 31264. After we will calculate the factors of 31248 and 31264 and find the biggest common factor number .

Step-1: Prime Factorization of 31248

Prime factors of 31248 are 2, 3, 7, 31. Prime factorization of 31248 in exponential form is:

31248 = 2⁴ × 3² × 7¹ × 31¹

Step-2: Prime Factorization of 31264

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

31264 = 2⁵ × 977¹

Step-3: Factors of 31248

List of positive integer factors of 31248 that divides 31248 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 31, 36, 42, 48, 56, 62, 63, 72, 84, 93, 112, 124, 126, 144, 168, 186, 217, 248, 252, 279, 336, 372, 434, 496, 504, 558, 651, 744, 868, 1008, 1116, 1302, 1488, 1736, 1953, 2232, 2604, 3472, 3906, 4464, 5208, 7812, 10416, 15624

Step-4: Factors of 31264

List of positive integer factors of 31264 that divides 31248 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31248 and 31264. The biggest common factor number is the GCF number.
So the greatest common factor 31248 and 31264 is 16.

Also check out the Least Common Multiple of 31248 and 31264