What is the Greatest Common Factor of 31570 and 31584?

Greatest common factor (GCF) of 31570 and 31584 is 14.

GCF(31570,31584) = 14

We will now calculate the prime factors of 31570 and 31584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31570 and 31584.

How to find the GCF of 31570 and 31584?

We will first find the prime factorization of 31570 and 31584. After we will calculate the factors of 31570 and 31584 and find the biggest common factor number .

Step-1: Prime Factorization of 31570

Prime factors of 31570 are 2, 5, 7, 11, 41. Prime factorization of 31570 in exponential form is:

31570 = 2¹ × 5¹ × 7¹ × 11¹ × 41¹

Step-2: 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-3: Factors of 31570

List of positive integer factors of 31570 that divides 31570 without a remainder.

1, 2, 5, 7, 10, 11, 14, 22, 35, 41, 55, 70, 77, 82, 110, 154, 205, 287, 385, 410, 451, 574, 770, 902, 1435, 2255, 2870, 3157, 4510, 6314, 15785

Step-4: Factors of 31584

List of positive integer factors of 31584 that divides 31570 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31570 and 31584. The biggest common factor number is the GCF number.
So the greatest common factor 31570 and 31584 is 14.

Also check out the Least Common Multiple of 31570 and 31584