What is the Greatest Common Factor of 1634 and 1638?

Greatest common factor (GCF) of 1634 and 1638 is 2.

GCF(1634,1638) = 2

We will now calculate the prime factors of 1634 and 1638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1634 and 1638.

How to find the GCF of 1634 and 1638?

We will first find the prime factorization of 1634 and 1638. After we will calculate the factors of 1634 and 1638 and find the biggest common factor number .

Step-1: Prime Factorization of 1634

Prime factors of 1634 are 2, 19, 43. Prime factorization of 1634 in exponential form is:

1634 = 2¹ × 19¹ × 43¹

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 1634

List of positive integer factors of 1634 that divides 1634 without a remainder.

1, 2, 19, 38, 43, 86, 817

Step-4: Factors of 1638

List of positive integer factors of 1638 that divides 1634 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 1634 and 1638. The biggest common factor number is the GCF number.
So the greatest common factor 1634 and 1638 is 2.

Also check out the Least Common Multiple of 1634 and 1638