What is the Greatest Common Factor of 1644 and 1659?

Greatest common factor (GCF) of 1644 and 1659 is 3.

GCF(1644,1659) = 3

We will now calculate the prime factors of 1644 and 1659, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1644 and 1659.

How to find the GCF of 1644 and 1659?

We will first find the prime factorization of 1644 and 1659. After we will calculate the factors of 1644 and 1659 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 1659

Prime factors of 1659 are 3, 7, 79. Prime factorization of 1659 in exponential form is:

1659 = 3¹ × 7¹ × 79¹

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 1659

List of positive integer factors of 1659 that divides 1644 without a remainder.

1, 3, 7, 21, 79, 237, 553

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1644 and 1659. The biggest common factor number is the GCF number.
So the greatest common factor 1644 and 1659 is 3.

Also check out the Least Common Multiple of 1644 and 1659