What is the Greatest Common Factor of 546 and 560?

Greatest common factor (GCF) of 546 and 560 is 14.

GCF(546,560) = 14

We will now calculate the prime factors of 546 and 560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 546 and 560.

How to find the GCF of 546 and 560?

We will first find the prime factorization of 546 and 560. After we will calculate the factors of 546 and 560 and find the biggest common factor number .

Step-1: Prime Factorization of 546

Prime factors of 546 are 2, 3, 7, 13. Prime factorization of 546 in exponential form is:

546 = 2¹ × 3¹ × 7¹ × 13¹

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 546

List of positive integer factors of 546 that divides 546 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273

Step-4: Factors of 560

List of positive integer factors of 560 that divides 546 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 546 and 560. The biggest common factor number is the GCF number.
So the greatest common factor 546 and 560 is 14.

Also check out the Least Common Multiple of 546 and 560