What is the Greatest Common Factor of 9960 and 9965?

Greatest common factor (GCF) of 9960 and 9965 is 5.

GCF(9960,9965) = 5

We will now calculate the prime factors of 9960 and 9965, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9960 and 9965.

How to find the GCF of 9960 and 9965?

We will first find the prime factorization of 9960 and 9965. After we will calculate the factors of 9960 and 9965 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 9965

Prime factors of 9965 are 5, 1993. Prime factorization of 9965 in exponential form is:

9965 = 5¹ × 1993¹

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 9965

List of positive integer factors of 9965 that divides 9960 without a remainder.

1, 5, 1993

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9960 and 9965. The biggest common factor number is the GCF number.
So the greatest common factor 9960 and 9965 is 5.

Also check out the Least Common Multiple of 9960 and 9965