What is the Greatest Common Factor of 34365 and 34380?

Greatest common factor (GCF) of 34365 and 34380 is 15.

GCF(34365,34380) = 15

We will now calculate the prime factors of 34365 and 34380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34365 and 34380.

How to find the GCF of 34365 and 34380?

We will first find the prime factorization of 34365 and 34380. After we will calculate the factors of 34365 and 34380 and find the biggest common factor number .

Step-1: Prime Factorization of 34365

Prime factors of 34365 are 3, 5, 29, 79. Prime factorization of 34365 in exponential form is:

34365 = 3¹ × 5¹ × 29¹ × 79¹

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 34365

List of positive integer factors of 34365 that divides 34365 without a remainder.

1, 3, 5, 15, 29, 79, 87, 145, 237, 395, 435, 1185, 2291, 6873, 11455

Step-4: Factors of 34380

List of positive integer factors of 34380 that divides 34365 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 34365 and 34380. The biggest common factor number is the GCF number.
So the greatest common factor 34365 and 34380 is 15.

Also check out the Least Common Multiple of 34365 and 34380