What is the Greatest Common Factor of 60200 and 60214?

Greatest common factor (GCF) of 60200 and 60214 is 14.

GCF(60200,60214) = 14

We will now calculate the prime factors of 60200 and 60214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 60200 and 60214.

How to find the GCF of 60200 and 60214?

We will first find the prime factorization of 60200 and 60214. After we will calculate the factors of 60200 and 60214 and find the biggest common factor number .

Step-1: Prime Factorization of 60200

Prime factors of 60200 are 2, 5, 7, 43. Prime factorization of 60200 in exponential form is:

60200 = 2³ × 5² × 7¹ × 43¹

Step-2: Prime Factorization of 60214

Prime factors of 60214 are 2, 7, 11, 17, 23. Prime factorization of 60214 in exponential form is:

60214 = 2¹ × 7¹ × 11¹ × 17¹ × 23¹

Step-3: Factors of 60200

List of positive integer factors of 60200 that divides 60200 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 43, 50, 56, 70, 86, 100, 140, 172, 175, 200, 215, 280, 301, 344, 350, 430, 602, 700, 860, 1075, 1204, 1400, 1505, 1720, 2150, 2408, 3010, 4300, 6020, 7525, 8600, 12040, 15050, 30100

Step-4: Factors of 60214

List of positive integer factors of 60214 that divides 60200 without a remainder.

1, 2, 7, 11, 14, 17, 22, 23, 34, 46, 77, 119, 154, 161, 187, 238, 253, 322, 374, 391, 506, 782, 1309, 1771, 2618, 2737, 3542, 4301, 5474, 8602, 30107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 60200 and 60214. The biggest common factor number is the GCF number.
So the greatest common factor 60200 and 60214 is 14.

Also check out the Least Common Multiple of 60200 and 60214