What is the Greatest Common Factor of 1635 and 1644?

Greatest common factor (GCF) of 1635 and 1644 is 3.

GCF(1635,1644) = 3

We will now calculate the prime factors of 1635 and 1644, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1635 and 1644.

How to find the GCF of 1635 and 1644?

We will first find the prime factorization of 1635 and 1644. After we will calculate the factors of 1635 and 1644 and find the biggest common factor number .

Step-1: Prime Factorization of 1635

Prime factors of 1635 are 3, 5, 109. Prime factorization of 1635 in exponential form is:

1635 = 3¹ × 5¹ × 109¹

Step-2: 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-3: Factors of 1635

List of positive integer factors of 1635 that divides 1635 without a remainder.

1, 3, 5, 15, 109, 327, 545

Step-4: Factors of 1644

List of positive integer factors of 1644 that divides 1635 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1635 and 1644. The biggest common factor number is the GCF number.
So the greatest common factor 1635 and 1644 is 3.

Also check out the Least Common Multiple of 1635 and 1644