What is the Greatest Common Factor of 1632 and 1647?

Greatest common factor (GCF) of 1632 and 1647 is 3.

GCF(1632,1647) = 3

We will now calculate the prime factors of 1632 and 1647, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1632 and 1647.

How to find the GCF of 1632 and 1647?

We will first find the prime factorization of 1632 and 1647. After we will calculate the factors of 1632 and 1647 and find the biggest common factor number .

Step-1: Prime Factorization of 1632

Prime factors of 1632 are 2, 3, 17. Prime factorization of 1632 in exponential form is:

1632 = 2⁵ × 3¹ × 17¹

Step-2: Prime Factorization of 1647

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

1647 = 3³ × 61¹

Step-3: Factors of 1632

List of positive integer factors of 1632 that divides 1632 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96, 102, 136, 204, 272, 408, 544, 816

Step-4: Factors of 1647

List of positive integer factors of 1647 that divides 1632 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1632 and 1647. The biggest common factor number is the GCF number.
So the greatest common factor 1632 and 1647 is 3.

Also check out the Least Common Multiple of 1632 and 1647