What is the Greatest Common Factor of 5760 and 5765?

Greatest common factor (GCF) of 5760 and 5765 is 5.

GCF(5760,5765) = 5

We will now calculate the prime factors of 5760 and 5765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5760 and 5765.

How to find the GCF of 5760 and 5765?

We will first find the prime factorization of 5760 and 5765. After we will calculate the factors of 5760 and 5765 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5765

Prime factors of 5765 are 5, 1153. Prime factorization of 5765 in exponential form is:

5765 = 5¹ × 1153¹

Step-3: Factors of 5760

List of positive integer factors of 5760 that divides 5760 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

Step-4: Factors of 5765

List of positive integer factors of 5765 that divides 5760 without a remainder.

1, 5, 1153

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5760 and 5765. The biggest common factor number is the GCF number.
So the greatest common factor 5760 and 5765 is 5.

Also check out the Least Common Multiple of 5760 and 5765