What is the Greatest Common Factor of 1638 and 1646?

Greatest common factor (GCF) of 1638 and 1646 is 2.

GCF(1638,1646) = 2

We will now calculate the prime factors of 1638 and 1646, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1638 and 1646.

How to find the GCF of 1638 and 1646?

We will first find the prime factorization of 1638 and 1646. After we will calculate the factors of 1638 and 1646 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 1646

Prime factors of 1646 are 2, 823. Prime factorization of 1646 in exponential form is:

1646 = 2¹ × 823¹

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 1646

List of positive integer factors of 1646 that divides 1638 without a remainder.

1, 2, 823

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1638 and 1646. The biggest common factor number is the GCF number.
So the greatest common factor 1638 and 1646 is 2.

Also check out the Least Common Multiple of 1638 and 1646