What is the Greatest Common Factor of 538 and 546?

Greatest common factor (GCF) of 538 and 546 is 2.

GCF(538,546) = 2

We will now calculate the prime factors of 538 and 546, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 538 and 546.

How to find the GCF of 538 and 546?

We will first find the prime factorization of 538 and 546. After we will calculate the factors of 538 and 546 and find the biggest common factor number .

Step-1: Prime Factorization of 538

Prime factors of 538 are 2, 269. Prime factorization of 538 in exponential form is:

538 = 2¹ × 269¹

Step-2: 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-3: Factors of 538

List of positive integer factors of 538 that divides 538 without a remainder.

1, 2, 269

Step-4: Factors of 546

List of positive integer factors of 546 that divides 538 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 538 and 546. The biggest common factor number is the GCF number.
So the greatest common factor 538 and 546 is 2.

Also check out the Least Common Multiple of 538 and 546