What is the Greatest Common Factor of 31905 and 31920?

Greatest common factor (GCF) of 31905 and 31920 is 15.

GCF(31905,31920) = 15

We will now calculate the prime factors of 31905 and 31920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31905 and 31920.

How to find the GCF of 31905 and 31920?

We will first find the prime factorization of 31905 and 31920. After we will calculate the factors of 31905 and 31920 and find the biggest common factor number .

Step-1: Prime Factorization of 31905

Prime factors of 31905 are 3, 5, 709. Prime factorization of 31905 in exponential form is:

31905 = 3² × 5¹ × 709¹

Step-2: 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-3: Factors of 31905

List of positive integer factors of 31905 that divides 31905 without a remainder.

1, 3, 5, 9, 15, 45, 709, 2127, 3545, 6381, 10635

Step-4: Factors of 31920

List of positive integer factors of 31920 that divides 31905 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31905 and 31920. The biggest common factor number is the GCF number.
So the greatest common factor 31905 and 31920 is 15.

Also check out the Least Common Multiple of 31905 and 31920