What is the Greatest Common Factor of 74214 and 74233?

Greatest common factor (GCF) of 74214 and 74233 is 19.

GCF(74214,74233) = 19

We will now calculate the prime factors of 74214 and 74233, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74214 and 74233.

How to find the GCF of 74214 and 74233?

We will first find the prime factorization of 74214 and 74233. After we will calculate the factors of 74214 and 74233 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 74233

Prime factors of 74233 are 19, 3907. Prime factorization of 74233 in exponential form is:

74233 = 19¹ × 3907¹

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 74233

List of positive integer factors of 74233 that divides 74214 without a remainder.

1, 19, 3907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74214 and 74233. The biggest common factor number is the GCF number.
So the greatest common factor 74214 and 74233 is 19.

Also check out the Least Common Multiple of 74214 and 74233