What is the Greatest Common Factor of 77200 and 77210?

Greatest common factor (GCF) of 77200 and 77210 is 10.

GCF(77200,77210) = 10

We will now calculate the prime factors of 77200 and 77210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77200 and 77210.

How to find the GCF of 77200 and 77210?

We will first find the prime factorization of 77200 and 77210. After we will calculate the factors of 77200 and 77210 and find the biggest common factor number .

Step-1: Prime Factorization of 77200

Prime factors of 77200 are 2, 5, 193. Prime factorization of 77200 in exponential form is:

77200 = 2⁴ × 5² × 193¹

Step-2: Prime Factorization of 77210

Prime factors of 77210 are 2, 5, 7, 1103. Prime factorization of 77210 in exponential form is:

77210 = 2¹ × 5¹ × 7¹ × 1103¹

Step-3: Factors of 77200

List of positive integer factors of 77200 that divides 77200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 193, 200, 386, 400, 772, 965, 1544, 1930, 3088, 3860, 4825, 7720, 9650, 15440, 19300, 38600

Step-4: Factors of 77210

List of positive integer factors of 77210 that divides 77200 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 1103, 2206, 5515, 7721, 11030, 15442, 38605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77200 and 77210. The biggest common factor number is the GCF number.
So the greatest common factor 77200 and 77210 is 10.

Also check out the Least Common Multiple of 77200 and 77210