What is the Greatest Common Factor of 1634 and 1653?

Greatest common factor (GCF) of 1634 and 1653 is 19.

GCF(1634,1653) = 19

We will now calculate the prime factors of 1634 and 1653, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1634 and 1653.

How to find the GCF of 1634 and 1653?

We will first find the prime factorization of 1634 and 1653. After we will calculate the factors of 1634 and 1653 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 1653

Prime factors of 1653 are 3, 19, 29. Prime factorization of 1653 in exponential form is:

1653 = 3¹ × 19¹ × 29¹

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 1653

List of positive integer factors of 1653 that divides 1634 without a remainder.

1, 3, 19, 29, 57, 87, 551

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1634 and 1653. The biggest common factor number is the GCF number.
So the greatest common factor 1634 and 1653 is 19.

Also check out the Least Common Multiple of 1634 and 1653