What is the Greatest Common Factor of 560 and 574?

Greatest common factor (GCF) of 560 and 574 is 14.

GCF(560,574) = 14

We will now calculate the prime factors of 560 and 574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 560 and 574.

How to find the GCF of 560 and 574?

We will first find the prime factorization of 560 and 574. After we will calculate the factors of 560 and 574 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 574

Prime factors of 574 are 2, 7, 41. Prime factorization of 574 in exponential form is:

574 = 2¹ × 7¹ × 41¹

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 574

List of positive integer factors of 574 that divides 560 without a remainder.

1, 2, 7, 14, 41, 82, 287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 560 and 574. The biggest common factor number is the GCF number.
So the greatest common factor 560 and 574 is 14.

Also check out the Least Common Multiple of 560 and 574