What is the Greatest Common Factor of 31976 and 31980?

Greatest common factor (GCF) of 31976 and 31980 is 4.

GCF(31976,31980) = 4

We will now calculate the prime factors of 31976 and 31980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31976 and 31980.

How to find the GCF of 31976 and 31980?

We will first find the prime factorization of 31976 and 31980. After we will calculate the factors of 31976 and 31980 and find the biggest common factor number .

Step-1: Prime Factorization of 31976

Prime factors of 31976 are 2, 7, 571. Prime factorization of 31976 in exponential form is:

31976 = 2³ × 7¹ × 571¹

Step-2: Prime Factorization of 31980

Prime factors of 31980 are 2, 3, 5, 13, 41. Prime factorization of 31980 in exponential form is:

31980 = 2² × 3¹ × 5¹ × 13¹ × 41¹

Step-3: Factors of 31976

List of positive integer factors of 31976 that divides 31976 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 571, 1142, 2284, 3997, 4568, 7994, 15988

Step-4: Factors of 31980

List of positive integer factors of 31980 that divides 31976 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 41, 52, 60, 65, 78, 82, 123, 130, 156, 164, 195, 205, 246, 260, 390, 410, 492, 533, 615, 780, 820, 1066, 1230, 1599, 2132, 2460, 2665, 3198, 5330, 6396, 7995, 10660, 15990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31976 and 31980. The biggest common factor number is the GCF number.
So the greatest common factor 31976 and 31980 is 4.

Also check out the Least Common Multiple of 31976 and 31980