What is the Greatest Common Factor of 31575 and 31590?

Greatest common factor (GCF) of 31575 and 31590 is 15.

GCF(31575,31590) = 15

We will now calculate the prime factors of 31575 and 31590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31575 and 31590.

How to find the GCF of 31575 and 31590?

We will first find the prime factorization of 31575 and 31590. After we will calculate the factors of 31575 and 31590 and find the biggest common factor number .

Step-1: Prime Factorization of 31575

Prime factors of 31575 are 3, 5, 421. Prime factorization of 31575 in exponential form is:

31575 = 3¹ × 5² × 421¹

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 31575

List of positive integer factors of 31575 that divides 31575 without a remainder.

1, 3, 5, 15, 25, 75, 421, 1263, 2105, 6315, 10525

Step-4: Factors of 31590

List of positive integer factors of 31590 that divides 31575 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 31575 and 31590. The biggest common factor number is the GCF number.
So the greatest common factor 31575 and 31590 is 15.

Also check out the Least Common Multiple of 31575 and 31590