What is the Greatest Common Factor of 560 and 578?

Greatest common factor (GCF) of 560 and 578 is 2.

GCF(560,578) = 2

We will now calculate the prime factors of 560 and 578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 560 and 578.

How to find the GCF of 560 and 578?

We will first find the prime factorization of 560 and 578. After we will calculate the factors of 560 and 578 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 578

Prime factors of 578 are 2, 17. Prime factorization of 578 in exponential form is:

578 = 2¹ × 17²

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 578

List of positive integer factors of 578 that divides 560 without a remainder.

1, 2, 17, 34, 289

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 560 and 578. The biggest common factor number is the GCF number.
So the greatest common factor 560 and 578 is 2.

Also check out the Least Common Multiple of 560 and 578