What is the Greatest Common Factor of 234 and 546?

Greatest common factor (GCF) of 234 and 546 is 78.

GCF(234,546) = 78

We will now calculate the prime factors of 234 and 546, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 234 and 546.

How to find the GCF of 234 and 546?

We will first find the prime factorization of 234 and 546. After we will calculate the factors of 234 and 546 and find the biggest common factor number .

Step-1: Prime Factorization of 234

Prime factors of 234 are 2, 3, 13. Prime factorization of 234 in exponential form is:

234 = 2¹ × 3² × 13¹

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 234

List of positive integer factors of 234 that divides 234 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117

Step-4: Factors of 546

List of positive integer factors of 546 that divides 234 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 234 and 546. The biggest common factor number is the GCF number.
So the greatest common factor 234 and 546 is 78.

Also check out the Least Common Multiple of 234 and 546