What is the Greatest Common Factor of 31980 and 31993?

Greatest common factor (GCF) of 31980 and 31993 is 13.

GCF(31980,31993) = 13

We will now calculate the prime factors of 31980 and 31993, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31980 and 31993.

How to find the GCF of 31980 and 31993?

We will first find the prime factorization of 31980 and 31993. After we will calculate the factors of 31980 and 31993 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 31993

Prime factors of 31993 are 13, 23, 107. Prime factorization of 31993 in exponential form is:

31993 = 13¹ × 23¹ × 107¹

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 31993

List of positive integer factors of 31993 that divides 31980 without a remainder.

1, 13, 23, 107, 299, 1391, 2461

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31980 and 31993. The biggest common factor number is the GCF number.
So the greatest common factor 31980 and 31993 is 13.

Also check out the Least Common Multiple of 31980 and 31993