What is the Greatest Common Factor of 74175 and 74180?

Greatest common factor (GCF) of 74175 and 74180 is 5.

GCF(74175,74180) = 5

We will now calculate the prime factors of 74175 and 74180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74175 and 74180.

How to find the GCF of 74175 and 74180?

We will first find the prime factorization of 74175 and 74180. After we will calculate the factors of 74175 and 74180 and find the biggest common factor number .

Step-1: Prime Factorization of 74175

Prime factors of 74175 are 3, 5, 23, 43. Prime factorization of 74175 in exponential form is:

74175 = 3¹ × 5² × 23¹ × 43¹

Step-2: Prime Factorization of 74180

Prime factors of 74180 are 2, 5, 3709. Prime factorization of 74180 in exponential form is:

74180 = 2² × 5¹ × 3709¹

Step-3: Factors of 74175

List of positive integer factors of 74175 that divides 74175 without a remainder.

1, 3, 5, 15, 23, 25, 43, 69, 75, 115, 129, 215, 345, 575, 645, 989, 1075, 1725, 2967, 3225, 4945, 14835, 24725

Step-4: Factors of 74180

List of positive integer factors of 74180 that divides 74175 without a remainder.

1, 2, 4, 5, 10, 20, 3709, 7418, 14836, 18545, 37090

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74175 and 74180. The biggest common factor number is the GCF number.
So the greatest common factor 74175 and 74180 is 5.

Also check out the Least Common Multiple of 74175 and 74180