What is the Greatest Common Factor of 945 and 960?

Greatest common factor (GCF) of 945 and 960 is 15.

GCF(945,960) = 15

We will now calculate the prime factors of 945 and 960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 945 and 960.

How to find the GCF of 945 and 960?

We will first find the prime factorization of 945 and 960. After we will calculate the factors of 945 and 960 and find the biggest common factor number .

Step-1: Prime Factorization of 945

Prime factors of 945 are 3, 5, 7. Prime factorization of 945 in exponential form is:

945 = 3³ × 5¹ × 7¹

Step-2: Prime Factorization of 960

Prime factors of 960 are 2, 3, 5. Prime factorization of 960 in exponential form is:

960 = 2⁶ × 3¹ × 5¹

Step-3: Factors of 945

List of positive integer factors of 945 that divides 945 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315

Step-4: Factors of 960

List of positive integer factors of 960 that divides 945 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 945 and 960. The biggest common factor number is the GCF number.
So the greatest common factor 945 and 960 is 15.

Also check out the Least Common Multiple of 945 and 960