What is the Greatest Common Factor of 78200 and 78210?

Greatest common factor (GCF) of 78200 and 78210 is 10.

GCF(78200,78210) = 10

We will now calculate the prime factors of 78200 and 78210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78200 and 78210.

How to find the GCF of 78200 and 78210?

We will first find the prime factorization of 78200 and 78210. After we will calculate the factors of 78200 and 78210 and find the biggest common factor number .

Step-1: Prime Factorization of 78200

Prime factors of 78200 are 2, 5, 17, 23. Prime factorization of 78200 in exponential form is:

78200 = 2³ × 5² × 17¹ × 23¹

Step-2: Prime Factorization of 78210

Prime factors of 78210 are 2, 3, 5, 11, 79. Prime factorization of 78210 in exponential form is:

78210 = 2¹ × 3² × 5¹ × 11¹ × 79¹

Step-3: Factors of 78200

List of positive integer factors of 78200 that divides 78200 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 23, 25, 34, 40, 46, 50, 68, 85, 92, 100, 115, 136, 170, 184, 200, 230, 340, 391, 425, 460, 575, 680, 782, 850, 920, 1150, 1564, 1700, 1955, 2300, 3128, 3400, 3910, 4600, 7820, 9775, 15640, 19550, 39100

Step-4: Factors of 78210

List of positive integer factors of 78210 that divides 78200 without a remainder.

1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 79, 90, 99, 110, 158, 165, 198, 237, 330, 395, 474, 495, 711, 790, 869, 990, 1185, 1422, 1738, 2370, 2607, 3555, 4345, 5214, 7110, 7821, 8690, 13035, 15642, 26070, 39105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78200 and 78210. The biggest common factor number is the GCF number.
So the greatest common factor 78200 and 78210 is 10.

Also check out the Least Common Multiple of 78200 and 78210