What is the Greatest Common Factor of 31584 and 31590?

Greatest common factor (GCF) of 31584 and 31590 is 6.

GCF(31584,31590) = 6

We will now calculate the prime factors of 31584 and 31590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31584 and 31590.

How to find the GCF of 31584 and 31590?

We will first find the prime factorization of 31584 and 31590. After we will calculate the factors of 31584 and 31590 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 31590

Prime factors of 31590 are 2, 3, 5, 13. Prime factorization of 31590 in exponential form is:

31590 = 2¹ × 3⁵ × 5¹ × 13¹

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 31590

List of positive integer factors of 31590 that divides 31584 without a remainder.

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 81, 90, 117, 130, 135, 162, 195, 234, 243, 270, 351, 390, 405, 486, 585, 702, 810, 1053, 1170, 1215, 1755, 2106, 2430, 3159, 3510, 5265, 6318, 10530, 15795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31584 and 31590. The biggest common factor number is the GCF number.
So the greatest common factor 31584 and 31590 is 6.

Also check out the Least Common Multiple of 31584 and 31590