What is the Greatest Common Factor of 31974 and 31980?

Greatest common factor (GCF) of 31974 and 31980 is 6.

GCF(31974,31980) = 6

We will now calculate the prime factors of 31974 and 31980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31974 and 31980.

How to find the GCF of 31974 and 31980?

We will first find the prime factorization of 31974 and 31980. After we will calculate the factors of 31974 and 31980 and find the biggest common factor number .

Step-1: Prime Factorization of 31974

Prime factors of 31974 are 2, 3, 73. Prime factorization of 31974 in exponential form is:

31974 = 2¹ × 3¹ × 73²

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 31974

List of positive integer factors of 31974 that divides 31974 without a remainder.

1, 2, 3, 6, 73, 146, 219, 438, 5329, 10658, 15987

Step-4: Factors of 31980

List of positive integer factors of 31980 that divides 31974 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 31974 and 31980. The biggest common factor number is the GCF number.
So the greatest common factor 31974 and 31980 is 6.

Also check out the Least Common Multiple of 31974 and 31980