What is the Greatest Common Factor of 1638 and 1652?

Greatest common factor (GCF) of 1638 and 1652 is 14.

GCF(1638,1652) = 14

We will now calculate the prime factors of 1638 and 1652, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1638 and 1652.

How to find the GCF of 1638 and 1652?

We will first find the prime factorization of 1638 and 1652. After we will calculate the factors of 1638 and 1652 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 1652

Prime factors of 1652 are 2, 7, 59. Prime factorization of 1652 in exponential form is:

1652 = 2² × 7¹ × 59¹

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 1652

List of positive integer factors of 1652 that divides 1638 without a remainder.

1, 2, 4, 7, 14, 28, 59, 118, 236, 413, 826

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1638 and 1652. The biggest common factor number is the GCF number.
So the greatest common factor 1638 and 1652 is 14.

Also check out the Least Common Multiple of 1638 and 1652