What is the Greatest Common Factor of 31563 and 31570?

Greatest common factor (GCF) of 31563 and 31570 is 7.

GCF(31563,31570) = 7

We will now calculate the prime factors of 31563 and 31570, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31563 and 31570.

How to find the GCF of 31563 and 31570?

We will first find the prime factorization of 31563 and 31570. After we will calculate the factors of 31563 and 31570 and find the biggest common factor number .

Step-1: Prime Factorization of 31563

Prime factors of 31563 are 3, 7, 167. Prime factorization of 31563 in exponential form is:

31563 = 3³ × 7¹ × 167¹

Step-2: 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-3: Factors of 31563

List of positive integer factors of 31563 that divides 31563 without a remainder.

1, 3, 7, 9, 21, 27, 63, 167, 189, 501, 1169, 1503, 3507, 4509, 10521

Step-4: Factors of 31570

List of positive integer factors of 31570 that divides 31563 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31563 and 31570. The biggest common factor number is the GCF number.
So the greatest common factor 31563 and 31570 is 7.

Also check out the Least Common Multiple of 31563 and 31570