What is the Greatest Common Factor of 1638 and 1644?

Greatest common factor (GCF) of 1638 and 1644 is 6.

GCF(1638,1644) = 6

We will now calculate the prime factors of 1638 and 1644, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1638 and 1644.

How to find the GCF of 1638 and 1644?

We will first find the prime factorization of 1638 and 1644. After we will calculate the factors of 1638 and 1644 and find the biggest common factor number .

Step-1: Prime Factorization of 1638

Prime factors of 1638 are 2, 3, 7, 13. Prime factorization of 1638 in exponential form is:

1638 = 2¹ × 3² × 7¹ × 13¹

Step-2: Prime Factorization of 1644

Prime factors of 1644 are 2, 3, 137. Prime factorization of 1644 in exponential form is:

1644 = 2² × 3¹ × 137¹

Step-3: Factors of 1638

List of positive integer factors of 1638 that divides 1638 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91, 117, 126, 182, 234, 273, 546, 819

Step-4: Factors of 1644

List of positive integer factors of 1644 that divides 1638 without a remainder.

1, 2, 3, 4, 6, 12, 137, 274, 411, 548, 822

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1638 and 1644. The biggest common factor number is the GCF number.
So the greatest common factor 1638 and 1644 is 6.

Also check out the Least Common Multiple of 1638 and 1644