What is the Greatest Common Factor of 29175 and 29184?

Greatest common factor (GCF) of 29175 and 29184 is 3.

GCF(29175,29184) = 3

We will now calculate the prime factors of 29175 and 29184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29175 and 29184.

How to find the GCF of 29175 and 29184?

We will first find the prime factorization of 29175 and 29184. After we will calculate the factors of 29175 and 29184 and find the biggest common factor number .

Step-1: Prime Factorization of 29175

Prime factors of 29175 are 3, 5, 389. Prime factorization of 29175 in exponential form is:

29175 = 3¹ × 5² × 389¹

Step-2: Prime Factorization of 29184

Prime factors of 29184 are 2, 3, 19. Prime factorization of 29184 in exponential form is:

29184 = 2⁹ × 3¹ × 19¹

Step-3: Factors of 29175

List of positive integer factors of 29175 that divides 29175 without a remainder.

1, 3, 5, 15, 25, 75, 389, 1167, 1945, 5835, 9725

Step-4: Factors of 29184

List of positive integer factors of 29184 that divides 29175 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 128, 152, 192, 228, 256, 304, 384, 456, 512, 608, 768, 912, 1216, 1536, 1824, 2432, 3648, 4864, 7296, 9728, 14592

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29175 and 29184. The biggest common factor number is the GCF number.
So the greatest common factor 29175 and 29184 is 3.

Also check out the Least Common Multiple of 29175 and 29184