What is the Greatest Common Factor of 35200 and 35212?

Greatest common factor (GCF) of 35200 and 35212 is 4.

GCF(35200,35212) = 4

We will now calculate the prime factors of 35200 and 35212, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35200 and 35212.

How to find the GCF of 35200 and 35212?

We will first find the prime factorization of 35200 and 35212. After we will calculate the factors of 35200 and 35212 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 35212

Prime factors of 35212 are 2, 8803. Prime factorization of 35212 in exponential form is:

35212 = 2² × 8803¹

Step-3: Factors of 35200

List of positive integer factors of 35200 that divides 35200 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

Step-4: Factors of 35212

List of positive integer factors of 35212 that divides 35200 without a remainder.

1, 2, 4, 8803, 17606

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35200 and 35212. The biggest common factor number is the GCF number.
So the greatest common factor 35200 and 35212 is 4.

Also check out the Least Common Multiple of 35200 and 35212