What is the Greatest Common Factor of 35205 and 35220?

Greatest common factor (GCF) of 35205 and 35220 is 15.

GCF(35205,35220) = 15

We will now calculate the prime factors of 35205 and 35220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35205 and 35220.

How to find the GCF of 35205 and 35220?

We will first find the prime factorization of 35205 and 35220. After we will calculate the factors of 35205 and 35220 and find the biggest common factor number .

Step-1: Prime Factorization of 35205

Prime factors of 35205 are 3, 5, 2347. Prime factorization of 35205 in exponential form is:

35205 = 3¹ × 5¹ × 2347¹

Step-2: Prime Factorization of 35220

Prime factors of 35220 are 2, 3, 5, 587. Prime factorization of 35220 in exponential form is:

35220 = 2² × 3¹ × 5¹ × 587¹

Step-3: Factors of 35205

List of positive integer factors of 35205 that divides 35205 without a remainder.

1, 3, 5, 15, 2347, 7041, 11735

Step-4: Factors of 35220

List of positive integer factors of 35220 that divides 35205 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 587, 1174, 1761, 2348, 2935, 3522, 5870, 7044, 8805, 11740, 17610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35205 and 35220. The biggest common factor number is the GCF number.
So the greatest common factor 35205 and 35220 is 15.

Also check out the Least Common Multiple of 35205 and 35220