What is the Greatest Common Factor of 9971 and 9984?

Greatest common factor (GCF) of 9971 and 9984 is 13.

GCF(9971,9984) = 13

We will now calculate the prime factors of 9971 and 9984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9971 and 9984.

How to find the GCF of 9971 and 9984?

We will first find the prime factorization of 9971 and 9984. After we will calculate the factors of 9971 and 9984 and find the biggest common factor number .

Step-1: Prime Factorization of 9971

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

9971 = 13² × 59¹

Step-2: Prime Factorization of 9984

Prime factors of 9984 are 2, 3, 13. Prime factorization of 9984 in exponential form is:

9984 = 2⁸ × 3¹ × 13¹

Step-3: Factors of 9971

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

1, 13, 59, 169, 767

Step-4: Factors of 9984

List of positive integer factors of 9984 that divides 9971 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9971 and 9984. The biggest common factor number is the GCF number.
So the greatest common factor 9971 and 9984 is 13.

Also check out the Least Common Multiple of 9971 and 9984