What is the Greatest Common Factor of 74460 and 74475?

Greatest common factor (GCF) of 74460 and 74475 is 15.

GCF(74460,74475) = 15

We will now calculate the prime factors of 74460 and 74475, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74460 and 74475.

How to find the GCF of 74460 and 74475?

We will first find the prime factorization of 74460 and 74475. After we will calculate the factors of 74460 and 74475 and find the biggest common factor number .

Step-1: Prime Factorization of 74460

Prime factors of 74460 are 2, 3, 5, 17, 73. Prime factorization of 74460 in exponential form is:

74460 = 2² × 3¹ × 5¹ × 17¹ × 73¹

Step-2: Prime Factorization of 74475

Prime factors of 74475 are 3, 5, 331. Prime factorization of 74475 in exponential form is:

74475 = 3² × 5² × 331¹

Step-3: Factors of 74460

List of positive integer factors of 74460 that divides 74460 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 73, 85, 102, 146, 170, 204, 219, 255, 292, 340, 365, 438, 510, 730, 876, 1020, 1095, 1241, 1460, 2190, 2482, 3723, 4380, 4964, 6205, 7446, 12410, 14892, 18615, 24820, 37230

Step-4: Factors of 74475

List of positive integer factors of 74475 that divides 74460 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 331, 993, 1655, 2979, 4965, 8275, 14895, 24825

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74460 and 74475. The biggest common factor number is the GCF number.
So the greatest common factor 74460 and 74475 is 15.

Also check out the Least Common Multiple of 74460 and 74475