What is the Greatest Common Factor of 1647 and 1665?

Greatest common factor (GCF) of 1647 and 1665 is 9.

GCF(1647,1665) = 9

We will now calculate the prime factors of 1647 and 1665, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1647 and 1665.

How to find the GCF of 1647 and 1665?

We will first find the prime factorization of 1647 and 1665. After we will calculate the factors of 1647 and 1665 and find the biggest common factor number .

Step-1: Prime Factorization of 1647

Prime factors of 1647 are 3, 61. Prime factorization of 1647 in exponential form is:

1647 = 3³ × 61¹

Step-2: Prime Factorization of 1665

Prime factors of 1665 are 3, 5, 37. Prime factorization of 1665 in exponential form is:

1665 = 3² × 5¹ × 37¹

Step-3: Factors of 1647

List of positive integer factors of 1647 that divides 1647 without a remainder.

1, 3, 9, 27, 61, 183, 549

Step-4: Factors of 1665

List of positive integer factors of 1665 that divides 1647 without a remainder.

1, 3, 5, 9, 15, 37, 45, 111, 185, 333, 555

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1647 and 1665. The biggest common factor number is the GCF number.
So the greatest common factor 1647 and 1665 is 9.

Also check out the Least Common Multiple of 1647 and 1665