What is the Greatest Common Factor of 29475 and 29484?

Greatest common factor (GCF) of 29475 and 29484 is 9.

GCF(29475,29484) = 9

We will now calculate the prime factors of 29475 and 29484, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29475 and 29484.

How to find the GCF of 29475 and 29484?

We will first find the prime factorization of 29475 and 29484. After we will calculate the factors of 29475 and 29484 and find the biggest common factor number .

Step-1: Prime Factorization of 29475

Prime factors of 29475 are 3, 5, 131. Prime factorization of 29475 in exponential form is:

29475 = 3² × 5² × 131¹

Step-2: Prime Factorization of 29484

Prime factors of 29484 are 2, 3, 7, 13. Prime factorization of 29484 in exponential form is:

29484 = 2² × 3⁴ × 7¹ × 13¹

Step-3: Factors of 29475

List of positive integer factors of 29475 that divides 29475 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 131, 225, 393, 655, 1179, 1965, 3275, 5895, 9825

Step-4: Factors of 29484

List of positive integer factors of 29484 that divides 29475 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 26, 27, 28, 36, 39, 42, 52, 54, 63, 78, 81, 84, 91, 108, 117, 126, 156, 162, 182, 189, 234, 252, 273, 324, 351, 364, 378, 468, 546, 567, 702, 756, 819, 1053, 1092, 1134, 1404, 1638, 2106, 2268, 2457, 3276, 4212, 4914, 7371, 9828, 14742

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29475 and 29484. The biggest common factor number is the GCF number.
So the greatest common factor 29475 and 29484 is 9.

Also check out the Least Common Multiple of 29475 and 29484