What is the Greatest Common Factor of 74188 and 74200?

Greatest common factor (GCF) of 74188 and 74200 is 4.

GCF(74188,74200) = 4

We will now calculate the prime factors of 74188 and 74200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74188 and 74200.

How to find the GCF of 74188 and 74200?

We will first find the prime factorization of 74188 and 74200. After we will calculate the factors of 74188 and 74200 and find the biggest common factor number .

Step-1: Prime Factorization of 74188

Prime factors of 74188 are 2, 17, 1091. Prime factorization of 74188 in exponential form is:

74188 = 2² × 17¹ × 1091¹

Step-2: 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-3: Factors of 74188

List of positive integer factors of 74188 that divides 74188 without a remainder.

1, 2, 4, 17, 34, 68, 1091, 2182, 4364, 18547, 37094

Step-4: Factors of 74200

List of positive integer factors of 74200 that divides 74188 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74188 and 74200. The biggest common factor number is the GCF number.
So the greatest common factor 74188 and 74200 is 4.

Also check out the Least Common Multiple of 74188 and 74200