What is the Greatest Common Factor of 560 and 575?

Greatest common factor (GCF) of 560 and 575 is 5.

GCF(560,575) = 5

We will now calculate the prime factors of 560 and 575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 560 and 575.

How to find the GCF of 560 and 575?

We will first find the prime factorization of 560 and 575. After we will calculate the factors of 560 and 575 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 575

Prime factors of 575 are 5, 23. Prime factorization of 575 in exponential form is:

575 = 5² × 23¹

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 575

List of positive integer factors of 575 that divides 560 without a remainder.

1, 5, 23, 25, 115

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 560 and 575. The biggest common factor number is the GCF number.
So the greatest common factor 560 and 575 is 5.

Also check out the Least Common Multiple of 560 and 575