What is the Greatest Common Factor of 35185 and 35200?

Greatest common factor (GCF) of 35185 and 35200 is 5.

GCF(35185,35200) = 5

We will now calculate the prime factors of 35185 and 35200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35185 and 35200.

How to find the GCF of 35185 and 35200?

We will first find the prime factorization of 35185 and 35200. After we will calculate the factors of 35185 and 35200 and find the biggest common factor number .

Step-1: Prime Factorization of 35185

Prime factors of 35185 are 5, 31, 227. Prime factorization of 35185 in exponential form is:

35185 = 5¹ × 31¹ × 227¹

Step-2: Prime Factorization of 35200

Prime factors of 35200 are 2, 5, 11. Prime factorization of 35200 in exponential form is:

35200 = 2⁷ × 5² × 11¹

Step-3: Factors of 35185

List of positive integer factors of 35185 that divides 35185 without a remainder.

1, 5, 31, 155, 227, 1135, 7037

Step-4: Factors of 35200

List of positive integer factors of 35200 that divides 35185 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 64, 80, 88, 100, 110, 128, 160, 176, 200, 220, 275, 320, 352, 400, 440, 550, 640, 704, 800, 880, 1100, 1408, 1600, 1760, 2200, 3200, 3520, 4400, 7040, 8800, 17600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35185 and 35200. The biggest common factor number is the GCF number.
So the greatest common factor 35185 and 35200 is 5.

Also check out the Least Common Multiple of 35185 and 35200