What is the Greatest Common Factor of 1617 and 1635?

Greatest common factor (GCF) of 1617 and 1635 is 3.

GCF(1617,1635) = 3

We will now calculate the prime factors of 1617 and 1635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1617 and 1635.

How to find the GCF of 1617 and 1635?

We will first find the prime factorization of 1617 and 1635. After we will calculate the factors of 1617 and 1635 and find the biggest common factor number .

Step-1: Prime Factorization of 1617

Prime factors of 1617 are 3, 7, 11. Prime factorization of 1617 in exponential form is:

1617 = 3¹ × 7² × 11¹

Step-2: 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-3: Factors of 1617

List of positive integer factors of 1617 that divides 1617 without a remainder.

1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539

Step-4: Factors of 1635

List of positive integer factors of 1635 that divides 1617 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1617 and 1635. The biggest common factor number is the GCF number.
So the greatest common factor 1617 and 1635 is 3.

Also check out the Least Common Multiple of 1617 and 1635