What is the Greatest Common Factor of 560 and 565?

Greatest common factor (GCF) of 560 and 565 is 5.

GCF(560,565) = 5

We will now calculate the prime factors of 560 and 565, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 560 and 565.

How to find the GCF of 560 and 565?

We will first find the prime factorization of 560 and 565. After we will calculate the factors of 560 and 565 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 565

Prime factors of 565 are 5, 113. Prime factorization of 565 in exponential form is:

565 = 5¹ × 113¹

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 565

List of positive integer factors of 565 that divides 560 without a remainder.

1, 5, 113

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 560 and 565. The biggest common factor number is the GCF number.
So the greatest common factor 560 and 565 is 5.

Also check out the Least Common Multiple of 560 and 565