What is the Greatest Common Factor of 1644 and 1656?

Greatest common factor (GCF) of 1644 and 1656 is 12.

GCF(1644,1656) = 12

We will now calculate the prime factors of 1644 and 1656, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1644 and 1656.

How to find the GCF of 1644 and 1656?

We will first find the prime factorization of 1644 and 1656. After we will calculate the factors of 1644 and 1656 and find the biggest common factor number .

Step-1: Prime Factorization of 1644

Prime factors of 1644 are 2, 3, 137. Prime factorization of 1644 in exponential form is:

1644 = 2² × 3¹ × 137¹

Step-2: 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-3: Factors of 1644

List of positive integer factors of 1644 that divides 1644 without a remainder.

1, 2, 3, 4, 6, 12, 137, 274, 411, 548, 822

Step-4: Factors of 1656

List of positive integer factors of 1656 that divides 1644 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1644 and 1656. The biggest common factor number is the GCF number.
So the greatest common factor 1644 and 1656 is 12.

Also check out the Least Common Multiple of 1644 and 1656