What is the Greatest Common Factor of 5751 and 5760?

Greatest common factor (GCF) of 5751 and 5760 is 9.

GCF(5751,5760) = 9

We will now calculate the prime factors of 5751 and 5760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5751 and 5760.

How to find the GCF of 5751 and 5760?

We will first find the prime factorization of 5751 and 5760. After we will calculate the factors of 5751 and 5760 and find the biggest common factor number .

Step-1: Prime Factorization of 5751

Prime factors of 5751 are 3, 71. Prime factorization of 5751 in exponential form is:

5751 = 3⁴ × 71¹

Step-2: Prime Factorization of 5760

Prime factors of 5760 are 2, 3, 5. Prime factorization of 5760 in exponential form is:

5760 = 2⁷ × 3² × 5¹

Step-3: Factors of 5751

List of positive integer factors of 5751 that divides 5751 without a remainder.

1, 3, 9, 27, 71, 81, 213, 639, 1917

Step-4: Factors of 5760

List of positive integer factors of 5760 that divides 5751 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5751 and 5760. The biggest common factor number is the GCF number.
So the greatest common factor 5751 and 5760 is 9.

Also check out the Least Common Multiple of 5751 and 5760