What is the Greatest Common Factor of 31584 and 31598?

Greatest common factor (GCF) of 31584 and 31598 is 14.

GCF(31584,31598) = 14

We will now calculate the prime factors of 31584 and 31598, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31584 and 31598.

How to find the GCF of 31584 and 31598?

We will first find the prime factorization of 31584 and 31598. After we will calculate the factors of 31584 and 31598 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 31598

Prime factors of 31598 are 2, 7, 37, 61. Prime factorization of 31598 in exponential form is:

31598 = 2¹ × 7¹ × 37¹ × 61¹

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 31598

List of positive integer factors of 31598 that divides 31584 without a remainder.

1, 2, 7, 14, 37, 61, 74, 122, 259, 427, 518, 854, 2257, 4514, 15799

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31584 and 31598. The biggest common factor number is the GCF number.
So the greatest common factor 31584 and 31598 is 14.

Also check out the Least Common Multiple of 31584 and 31598