What is the Greatest Common Factor of 74200 and 74214?

Greatest common factor (GCF) of 74200 and 74214 is 14.

GCF(74200,74214) = 14

We will now calculate the prime factors of 74200 and 74214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74200 and 74214.

How to find the GCF of 74200 and 74214?

We will first find the prime factorization of 74200 and 74214. After we will calculate the factors of 74200 and 74214 and find the biggest common factor number .

Step-1: Prime Factorization of 74200

Prime factors of 74200 are 2, 5, 7, 53. Prime factorization of 74200 in exponential form is:

74200 = 2³ × 5² × 7¹ × 53¹

Step-2: Prime Factorization of 74214

Prime factors of 74214 are 2, 3, 7, 19, 31. Prime factorization of 74214 in exponential form is:

74214 = 2¹ × 3² × 7¹ × 19¹ × 31¹

Step-3: Factors of 74200

List of positive integer factors of 74200 that divides 74200 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 53, 56, 70, 100, 106, 140, 175, 200, 212, 265, 280, 350, 371, 424, 530, 700, 742, 1060, 1325, 1400, 1484, 1855, 2120, 2650, 2968, 3710, 5300, 7420, 9275, 10600, 14840, 18550, 37100

Step-4: Factors of 74214

List of positive integer factors of 74214 that divides 74200 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 31, 38, 42, 57, 62, 63, 93, 114, 126, 133, 171, 186, 217, 266, 279, 342, 399, 434, 558, 589, 651, 798, 1178, 1197, 1302, 1767, 1953, 2394, 3534, 3906, 4123, 5301, 8246, 10602, 12369, 24738, 37107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74200 and 74214. The biggest common factor number is the GCF number.
So the greatest common factor 74200 and 74214 is 14.

Also check out the Least Common Multiple of 74200 and 74214