What is the Greatest Common Factor of 31920 and 31930?

Greatest common factor (GCF) of 31920 and 31930 is 10.

GCF(31920,31930) = 10

We will now calculate the prime factors of 31920 and 31930, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31920 and 31930.

How to find the GCF of 31920 and 31930?

We will first find the prime factorization of 31920 and 31930. After we will calculate the factors of 31920 and 31930 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 31930

Prime factors of 31930 are 2, 5, 31, 103. Prime factorization of 31930 in exponential form is:

31930 = 2¹ × 5¹ × 31¹ × 103¹

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 31930

List of positive integer factors of 31930 that divides 31920 without a remainder.

1, 2, 5, 10, 31, 62, 103, 155, 206, 310, 515, 1030, 3193, 6386, 15965

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31920 and 31930. The biggest common factor number is the GCF number.
So the greatest common factor 31920 and 31930 is 10.

Also check out the Least Common Multiple of 31920 and 31930