What is the Greatest Common Factor of 31584 and 31596?

Greatest common factor (GCF) of 31584 and 31596 is 12.

GCF(31584,31596) = 12

We will now calculate the prime factors of 31584 and 31596, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31584 and 31596.

How to find the GCF of 31584 and 31596?

We will first find the prime factorization of 31584 and 31596. After we will calculate the factors of 31584 and 31596 and find the biggest common factor number .

Step-1: Prime Factorization of 31584

Prime factors of 31584 are 2, 3, 7, 47. Prime factorization of 31584 in exponential form is:

31584 = 2⁵ × 3¹ × 7¹ × 47¹

Step-2: Prime Factorization of 31596

Prime factors of 31596 are 2, 3, 2633. Prime factorization of 31596 in exponential form is:

31596 = 2² × 3¹ × 2633¹

Step-3: Factors of 31584

List of positive integer factors of 31584 that divides 31584 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 47, 48, 56, 84, 94, 96, 112, 141, 168, 188, 224, 282, 329, 336, 376, 564, 658, 672, 752, 987, 1128, 1316, 1504, 1974, 2256, 2632, 3948, 4512, 5264, 7896, 10528, 15792

Step-4: Factors of 31596

List of positive integer factors of 31596 that divides 31584 without a remainder.

1, 2, 3, 4, 6, 12, 2633, 5266, 7899, 10532, 15798

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31584 and 31596. The biggest common factor number is the GCF number.
So the greatest common factor 31584 and 31596 is 12.

Also check out the Least Common Multiple of 31584 and 31596