What is the Greatest Common Factor of 1623 and 1638?

Greatest common factor (GCF) of 1623 and 1638 is 3.

GCF(1623,1638) = 3

We will now calculate the prime factors of 1623 and 1638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1623 and 1638.

How to find the GCF of 1623 and 1638?

We will first find the prime factorization of 1623 and 1638. After we will calculate the factors of 1623 and 1638 and find the biggest common factor number .

Step-1: Prime Factorization of 1623

Prime factors of 1623 are 3, 541. Prime factorization of 1623 in exponential form is:

1623 = 3¹ × 541¹

Step-2: 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-3: Factors of 1623

List of positive integer factors of 1623 that divides 1623 without a remainder.

1, 3, 541

Step-4: Factors of 1638

List of positive integer factors of 1638 that divides 1623 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1623 and 1638. The biggest common factor number is the GCF number.
So the greatest common factor 1623 and 1638 is 3.

Also check out the Least Common Multiple of 1623 and 1638