What is the Greatest Common Factor of 31472 and 31488?

Greatest common factor (GCF) of 31472 and 31488 is 16.

GCF(31472,31488) = 16

We will now calculate the prime factors of 31472 and 31488, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31472 and 31488.

How to find the GCF of 31472 and 31488?

We will first find the prime factorization of 31472 and 31488. After we will calculate the factors of 31472 and 31488 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31488

Prime factors of 31488 are 2, 3, 41. Prime factorization of 31488 in exponential form is:

31488 = 2⁸ × 3¹ × 41¹

Step-3: Factors of 31472

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

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

Step-4: Factors of 31488

List of positive integer factors of 31488 that divides 31472 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 64, 82, 96, 123, 128, 164, 192, 246, 256, 328, 384, 492, 656, 768, 984, 1312, 1968, 2624, 3936, 5248, 7872, 10496, 15744

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31472 and 31488. The biggest common factor number is the GCF number.
So the greatest common factor 31472 and 31488 is 16.

Also check out the Least Common Multiple of 31472 and 31488