What is the Greatest Common Factor of 9960 and 9971?

Greatest common factor (GCF) of 9960 and 9971 is 1.

GCF(9960,9971) = 1

We will now calculate the prime factors of 9960 and 9971, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9960 and 9971.

How to find the GCF of 9960 and 9971?

We will first find the prime factorization of 9960 and 9971. After we will calculate the factors of 9960 and 9971 and find the biggest common factor number .

Step-1: Prime Factorization of 9960

Prime factors of 9960 are 2, 3, 5, 83. Prime factorization of 9960 in exponential form is:

9960 = 2³ × 3¹ × 5¹ × 83¹

Step-2: Prime Factorization of 9971

Prime factors of 9971 are 13, 59. Prime factorization of 9971 in exponential form is:

9971 = 13² × 59¹

Step-3: Factors of 9960

List of positive integer factors of 9960 that divides 9960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83, 120, 166, 249, 332, 415, 498, 664, 830, 996, 1245, 1660, 1992, 2490, 3320, 4980

Step-4: Factors of 9971

List of positive integer factors of 9971 that divides 9960 without a remainder.

1, 13, 59, 169, 767

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9960 and 9971. The biggest common factor number is the GCF number.
So the greatest common factor 9960 and 9971 is 1.

Also check out the Least Common Multiple of 9960 and 9971