What is the Greatest Common Factor of 34375 and 34380?

Greatest common factor (GCF) of 34375 and 34380 is 5.

GCF(34375,34380) = 5

We will now calculate the prime factors of 34375 and 34380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34375 and 34380.

How to find the GCF of 34375 and 34380?

We will first find the prime factorization of 34375 and 34380. After we will calculate the factors of 34375 and 34380 and find the biggest common factor number .

Step-1: Prime Factorization of 34375

Prime factors of 34375 are 5, 11. Prime factorization of 34375 in exponential form is:

34375 = 5⁵ × 11¹

Step-2: Prime Factorization of 34380

Prime factors of 34380 are 2, 3, 5, 191. Prime factorization of 34380 in exponential form is:

34380 = 2² × 3² × 5¹ × 191¹

Step-3: Factors of 34375

List of positive integer factors of 34375 that divides 34375 without a remainder.

1, 5, 11, 25, 55, 125, 275, 625, 1375, 3125, 6875

Step-4: Factors of 34380

List of positive integer factors of 34380 that divides 34375 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 191, 382, 573, 764, 955, 1146, 1719, 1910, 2292, 2865, 3438, 3820, 5730, 6876, 8595, 11460, 17190

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34375 and 34380. The biggest common factor number is the GCF number.
So the greatest common factor 34375 and 34380 is 5.

Also check out the Least Common Multiple of 34375 and 34380