What is the Greatest Common Factor of 1656 and 1674?

Greatest common factor (GCF) of 1656 and 1674 is 18.

GCF(1656,1674) = 18

We will now calculate the prime factors of 1656 and 1674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1656 and 1674.

How to find the GCF of 1656 and 1674?

We will first find the prime factorization of 1656 and 1674. After we will calculate the factors of 1656 and 1674 and find the biggest common factor number .

Step-1: Prime Factorization of 1656

Prime factors of 1656 are 2, 3, 23. Prime factorization of 1656 in exponential form is:

1656 = 2³ × 3² × 23¹

Step-2: Prime Factorization of 1674

Prime factors of 1674 are 2, 3, 31. Prime factorization of 1674 in exponential form is:

1674 = 2¹ × 3³ × 31¹

Step-3: Factors of 1656

List of positive integer factors of 1656 that divides 1656 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828

Step-4: Factors of 1674

List of positive integer factors of 1674 that divides 1656 without a remainder.

1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1656 and 1674. The biggest common factor number is the GCF number.
So the greatest common factor 1656 and 1674 is 18.

Also check out the Least Common Multiple of 1656 and 1674