What is the Greatest Common Factor of 74214 and 74228?

Greatest common factor (GCF) of 74214 and 74228 is 14.

GCF(74214,74228) = 14

We will now calculate the prime factors of 74214 and 74228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74214 and 74228.

How to find the GCF of 74214 and 74228?

We will first find the prime factorization of 74214 and 74228. After we will calculate the factors of 74214 and 74228 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 74228

Prime factors of 74228 are 2, 7, 11, 241. Prime factorization of 74228 in exponential form is:

74228 = 2² × 7¹ × 11¹ × 241¹

Step-3: Factors of 74214

List of positive integer factors of 74214 that divides 74214 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

Step-4: Factors of 74228

List of positive integer factors of 74228 that divides 74214 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 241, 308, 482, 964, 1687, 2651, 3374, 5302, 6748, 10604, 18557, 37114

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74214 and 74228. The biggest common factor number is the GCF number.
So the greatest common factor 74214 and 74228 is 14.

Also check out the Least Common Multiple of 74214 and 74228