What is the Greatest Common Factor of 31464 and 31472?

Greatest common factor (GCF) of 31464 and 31472 is 8.

GCF(31464,31472) = 8

We will now calculate the prime factors of 31464 and 31472, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31464 and 31472.

How to find the GCF of 31464 and 31472?

We will first find the prime factorization of 31464 and 31472. After we will calculate the factors of 31464 and 31472 and find the biggest common factor number .

Step-1: Prime Factorization of 31464

Prime factors of 31464 are 2, 3, 19, 23. Prime factorization of 31464 in exponential form is:

31464 = 2³ × 3² × 19¹ × 23¹

Step-2: Prime Factorization of 31472

Prime factors of 31472 are 2, 7, 281. Prime factorization of 31472 in exponential form is:

31472 = 2⁴ × 7¹ × 281¹

Step-3: Factors of 31464

List of positive integer factors of 31464 that divides 31464 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 23, 24, 36, 38, 46, 57, 69, 72, 76, 92, 114, 138, 152, 171, 184, 207, 228, 276, 342, 414, 437, 456, 552, 684, 828, 874, 1311, 1368, 1656, 1748, 2622, 3496, 3933, 5244, 7866, 10488, 15732

Step-4: Factors of 31472

List of positive integer factors of 31472 that divides 31464 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 281, 562, 1124, 1967, 2248, 3934, 4496, 7868, 15736

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31464 and 31472. The biggest common factor number is the GCF number.
So the greatest common factor 31464 and 31472 is 8.

Also check out the Least Common Multiple of 31464 and 31472