What is the Greatest Common Factor of 35200 and 35210?

Greatest common factor (GCF) of 35200 and 35210 is 10.

GCF(35200,35210) = 10

We will now calculate the prime factors of 35200 and 35210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35200 and 35210.

How to find the GCF of 35200 and 35210?

We will first find the prime factorization of 35200 and 35210. After we will calculate the factors of 35200 and 35210 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 35210

Prime factors of 35210 are 2, 5, 7, 503. Prime factorization of 35210 in exponential form is:

35210 = 2¹ × 5¹ × 7¹ × 503¹

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 35210

List of positive integer factors of 35210 that divides 35200 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 503, 1006, 2515, 3521, 5030, 7042, 17605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35200 and 35210. The biggest common factor number is the GCF number.
So the greatest common factor 35200 and 35210 is 10.

Also check out the Least Common Multiple of 35200 and 35210