What is the Greatest Common Factor of 1614 and 1632?

Greatest common factor (GCF) of 1614 and 1632 is 6.

GCF(1614,1632) = 6

We will now calculate the prime factors of 1614 and 1632, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1614 and 1632.

How to find the GCF of 1614 and 1632?

We will first find the prime factorization of 1614 and 1632. After we will calculate the factors of 1614 and 1632 and find the biggest common factor number .

Step-1: Prime Factorization of 1614

Prime factors of 1614 are 2, 3, 269. Prime factorization of 1614 in exponential form is:

1614 = 2¹ × 3¹ × 269¹

Step-2: 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-3: Factors of 1614

List of positive integer factors of 1614 that divides 1614 without a remainder.

1, 2, 3, 6, 269, 538, 807

Step-4: Factors of 1632

List of positive integer factors of 1632 that divides 1614 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1614 and 1632. The biggest common factor number is the GCF number.
So the greatest common factor 1614 and 1632 is 6.

Also check out the Least Common Multiple of 1614 and 1632