What is the Greatest Common Factor of 1614 and 1629?

Greatest common factor (GCF) of 1614 and 1629 is 3.

GCF(1614,1629) = 3

We will now calculate the prime factors of 1614 and 1629, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1614 and 1629.

How to find the GCF of 1614 and 1629?

We will first find the prime factorization of 1614 and 1629. After we will calculate the factors of 1614 and 1629 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 1629

Prime factors of 1629 are 3, 181. Prime factorization of 1629 in exponential form is:

1629 = 3² × 181¹

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 1629

List of positive integer factors of 1629 that divides 1614 without a remainder.

1, 3, 9, 181, 543

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1614 and 1629. The biggest common factor number is the GCF number.
So the greatest common factor 1614 and 1629 is 3.

Also check out the Least Common Multiple of 1614 and 1629