What is the Greatest Common Factor of 540 and 560?

Greatest common factor (GCF) of 540 and 560 is 20.

GCF(540,560) = 20

We will now calculate the prime factors of 540 and 560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 540 and 560.

How to find the GCF of 540 and 560?

We will first find the prime factorization of 540 and 560. After we will calculate the factors of 540 and 560 and find the biggest common factor number .

Step-1: Prime Factorization of 540

Prime factors of 540 are 2, 3, 5. Prime factorization of 540 in exponential form is:

540 = 2² × 3³ × 5¹

Step-2: 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-3: Factors of 540

List of positive integer factors of 540 that divides 540 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270

Step-4: Factors of 560

List of positive integer factors of 560 that divides 540 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 540 and 560. The biggest common factor number is the GCF number.
So the greatest common factor 540 and 560 is 20.

Also check out the Least Common Multiple of 540 and 560