What is the Greatest Common Factor of 560 and 567?

Greatest common factor (GCF) of 560 and 567 is 7.

GCF(560,567) = 7

We will now calculate the prime factors of 560 and 567, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 560 and 567.

How to find the GCF of 560 and 567?

We will first find the prime factorization of 560 and 567. After we will calculate the factors of 560 and 567 and find the biggest common factor number .

Step-1: Prime Factorization of 560

Prime factors of 560 are 2, 5, 7. Prime factorization of 560 in exponential form is:

560 = 2⁴ × 5¹ × 7¹

Step-2: Prime Factorization of 567

Prime factors of 567 are 3, 7. Prime factorization of 567 in exponential form is:

567 = 3⁴ × 7¹

Step-3: Factors of 560

List of positive integer factors of 560 that divides 560 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280

Step-4: Factors of 567

List of positive integer factors of 567 that divides 560 without a remainder.

1, 3, 7, 9, 21, 27, 63, 81, 189

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 560 and 567. The biggest common factor number is the GCF number.
So the greatest common factor 560 and 567 is 7.

Also check out the Least Common Multiple of 560 and 567