What is the Greatest Common Factor of 69200 and 69210?

Greatest common factor (GCF) of 69200 and 69210 is 10.

GCF(69200,69210) = 10

We will now calculate the prime factors of 69200 and 69210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69200 and 69210.

How to find the GCF of 69200 and 69210?

We will first find the prime factorization of 69200 and 69210. After we will calculate the factors of 69200 and 69210 and find the biggest common factor number .

Step-1: Prime Factorization of 69200

Prime factors of 69200 are 2, 5, 173. Prime factorization of 69200 in exponential form is:

69200 = 2⁴ × 5² × 173¹

Step-2: Prime Factorization of 69210

Prime factors of 69210 are 2, 3, 5, 769. Prime factorization of 69210 in exponential form is:

69210 = 2¹ × 3² × 5¹ × 769¹

Step-3: Factors of 69200

List of positive integer factors of 69200 that divides 69200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 173, 200, 346, 400, 692, 865, 1384, 1730, 2768, 3460, 4325, 6920, 8650, 13840, 17300, 34600

Step-4: Factors of 69210

List of positive integer factors of 69210 that divides 69200 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 769, 1538, 2307, 3845, 4614, 6921, 7690, 11535, 13842, 23070, 34605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69200 and 69210. The biggest common factor number is the GCF number.
So the greatest common factor 69200 and 69210 is 10.

Also check out the Least Common Multiple of 69200 and 69210