What is the Greatest Common Factor of 9945 and 9960?

Greatest common factor (GCF) of 9945 and 9960 is 15.

GCF(9945,9960) = 15

We will now calculate the prime factors of 9945 and 9960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9945 and 9960.

How to find the GCF of 9945 and 9960?

We will first find the prime factorization of 9945 and 9960. After we will calculate the factors of 9945 and 9960 and find the biggest common factor number .

Step-1: Prime Factorization of 9945

Prime factors of 9945 are 3, 5, 13, 17. Prime factorization of 9945 in exponential form is:

9945 = 3² × 5¹ × 13¹ × 17¹

Step-2: 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-3: Factors of 9945

List of positive integer factors of 9945 that divides 9945 without a remainder.

1, 3, 5, 9, 13, 15, 17, 39, 45, 51, 65, 85, 117, 153, 195, 221, 255, 585, 663, 765, 1105, 1989, 3315

Step-4: Factors of 9960

List of positive integer factors of 9960 that divides 9945 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9945 and 9960. The biggest common factor number is the GCF number.
So the greatest common factor 9945 and 9960 is 15.

Also check out the Least Common Multiple of 9945 and 9960