What is the Greatest Common Factor of 42 and 57?

Greatest common factor (GCF) of 42 and 57 is 3.

GCF(42,57) = 3

We will now calculate the prime factors of 42 and 57, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42 and 57.

How to find the GCF of 42 and 57?

We will first find the prime factorization of 42 and 57. After we will calculate the factors of 42 and 57 and find the biggest common factor number .

Step-1: Prime Factorization of 42

Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:

42 = 2¹ × 3¹ × 7¹

Step-2: Prime Factorization of 57

Prime factors of 57 are 3, 19. Prime factorization of 57 in exponential form is:

57 = 3¹ × 19¹

Step-3: Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21

Step-4: Factors of 57

List of positive integer factors of 57 that divides 42 without a remainder.

1, 3, 19

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42 and 57. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 57 is 3.

Also check out the Least Common Multiple of 42 and 57