What is the Greatest Common Factor of 31980 and 31998?

Greatest common factor (GCF) of 31980 and 31998 is 6.

GCF(31980,31998) = 6

We will now calculate the prime factors of 31980 and 31998, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31980 and 31998.

How to find the GCF of 31980 and 31998?

We will first find the prime factorization of 31980 and 31998. After we will calculate the factors of 31980 and 31998 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31998

Prime factors of 31998 are 2, 3, 5333. Prime factorization of 31998 in exponential form is:

31998 = 2¹ × 3¹ × 5333¹

Step-3: Factors of 31980

List of positive integer factors of 31980 that divides 31980 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

Step-4: Factors of 31998

List of positive integer factors of 31998 that divides 31980 without a remainder.

1, 2, 3, 6, 5333, 10666, 15999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31980 and 31998. The biggest common factor number is the GCF number.
So the greatest common factor 31980 and 31998 is 6.

Also check out the Least Common Multiple of 31980 and 31998