What is the Greatest Common Factor of 31920 and 31935?

Greatest common factor (GCF) of 31920 and 31935 is 15.

GCF(31920,31935) = 15

We will now calculate the prime factors of 31920 and 31935, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31920 and 31935.

How to find the GCF of 31920 and 31935?

We will first find the prime factorization of 31920 and 31935. After we will calculate the factors of 31920 and 31935 and find the biggest common factor number .

Step-1: Prime Factorization of 31920

Prime factors of 31920 are 2, 3, 5, 7, 19. Prime factorization of 31920 in exponential form is:

31920 = 2⁴ × 3¹ × 5¹ × 7¹ × 19¹

Step-2: Prime Factorization of 31935

Prime factors of 31935 are 3, 5, 2129. Prime factorization of 31935 in exponential form is:

31935 = 3¹ × 5¹ × 2129¹

Step-3: Factors of 31920

List of positive integer factors of 31920 that divides 31920 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960

Step-4: Factors of 31935

List of positive integer factors of 31935 that divides 31920 without a remainder.

1, 3, 5, 15, 2129, 6387, 10645

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31920 and 31935. The biggest common factor number is the GCF number.
So the greatest common factor 31920 and 31935 is 15.

Also check out the Least Common Multiple of 31920 and 31935