What is the Greatest Common Factor of 11625 and 11634?

Greatest common factor (GCF) of 11625 and 11634 is 3.

GCF(11625,11634) = 3

We will now calculate the prime factors of 11625 and 11634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11625 and 11634.

How to find the GCF of 11625 and 11634?

We will first find the prime factorization of 11625 and 11634. After we will calculate the factors of 11625 and 11634 and find the biggest common factor number .

Step-1: Prime Factorization of 11625

Prime factors of 11625 are 3, 5, 31. Prime factorization of 11625 in exponential form is:

11625 = 3¹ × 5³ × 31¹

Step-2: Prime Factorization of 11634

Prime factors of 11634 are 2, 3, 7, 277. Prime factorization of 11634 in exponential form is:

11634 = 2¹ × 3¹ × 7¹ × 277¹

Step-3: Factors of 11625

List of positive integer factors of 11625 that divides 11625 without a remainder.

1, 3, 5, 15, 25, 31, 75, 93, 125, 155, 375, 465, 775, 2325, 3875

Step-4: Factors of 11634

List of positive integer factors of 11634 that divides 11625 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 277, 554, 831, 1662, 1939, 3878, 5817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11625 and 11634. The biggest common factor number is the GCF number.
So the greatest common factor 11625 and 11634 is 3.

Also check out the Least Common Multiple of 11625 and 11634