What is the Greatest Common Factor of 74375 and 74380?

Greatest common factor (GCF) of 74375 and 74380 is 5.

GCF(74375,74380) = 5

We will now calculate the prime factors of 74375 and 74380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74375 and 74380.

How to find the GCF of 74375 and 74380?

We will first find the prime factorization of 74375 and 74380. After we will calculate the factors of 74375 and 74380 and find the biggest common factor number .

Step-1: Prime Factorization of 74375

Prime factors of 74375 are 5, 7, 17. Prime factorization of 74375 in exponential form is:

74375 = 5⁴ × 7¹ × 17¹

Step-2: Prime Factorization of 74380

Prime factors of 74380 are 2, 5, 3719. Prime factorization of 74380 in exponential form is:

74380 = 2² × 5¹ × 3719¹

Step-3: Factors of 74375

List of positive integer factors of 74375 that divides 74375 without a remainder.

1, 5, 7, 17, 25, 35, 85, 119, 125, 175, 425, 595, 625, 875, 2125, 2975, 4375, 10625, 14875

Step-4: Factors of 74380

List of positive integer factors of 74380 that divides 74375 without a remainder.

1, 2, 4, 5, 10, 20, 3719, 7438, 14876, 18595, 37190

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74375 and 74380. The biggest common factor number is the GCF number.
So the greatest common factor 74375 and 74380 is 5.

Also check out the Least Common Multiple of 74375 and 74380