What is the Greatest Common Factor of 31584 and 31591?

Greatest common factor (GCF) of 31584 and 31591 is 7.

GCF(31584,31591) = 7

We will now calculate the prime factors of 31584 and 31591, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31584 and 31591.

How to find the GCF of 31584 and 31591?

We will first find the prime factorization of 31584 and 31591. After we will calculate the factors of 31584 and 31591 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 31591

Prime factors of 31591 are 7, 4513. Prime factorization of 31591 in exponential form is:

31591 = 7¹ × 4513¹

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 31591

List of positive integer factors of 31591 that divides 31584 without a remainder.

1, 7, 4513

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31584 and 31591. The biggest common factor number is the GCF number.
So the greatest common factor 31584 and 31591 is 7.

Also check out the Least Common Multiple of 31584 and 31591