What is the Greatest Common Factor of 29625 and 29634?

Greatest common factor (GCF) of 29625 and 29634 is 3.

GCF(29625,29634) = 3

We will now calculate the prime factors of 29625 and 29634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29625 and 29634.

How to find the GCF of 29625 and 29634?

We will first find the prime factorization of 29625 and 29634. After we will calculate the factors of 29625 and 29634 and find the biggest common factor number .

Step-1: Prime Factorization of 29625

Prime factors of 29625 are 3, 5, 79. Prime factorization of 29625 in exponential form is:

29625 = 3¹ × 5³ × 79¹

Step-2: Prime Factorization of 29634

Prime factors of 29634 are 2, 3, 11, 449. Prime factorization of 29634 in exponential form is:

29634 = 2¹ × 3¹ × 11¹ × 449¹

Step-3: Factors of 29625

List of positive integer factors of 29625 that divides 29625 without a remainder.

1, 3, 5, 15, 25, 75, 79, 125, 237, 375, 395, 1185, 1975, 5925, 9875

Step-4: Factors of 29634

List of positive integer factors of 29634 that divides 29625 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 449, 898, 1347, 2694, 4939, 9878, 14817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29625 and 29634. The biggest common factor number is the GCF number.
So the greatest common factor 29625 and 29634 is 3.

Also check out the Least Common Multiple of 29625 and 29634