What is the Greatest Common Factor of 74190 and 74200?

Greatest common factor (GCF) of 74190 and 74200 is 10.

GCF(74190,74200) = 10

We will now calculate the prime factors of 74190 and 74200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74190 and 74200.

How to find the GCF of 74190 and 74200?

We will first find the prime factorization of 74190 and 74200. After we will calculate the factors of 74190 and 74200 and find the biggest common factor number .

Step-1: Prime Factorization of 74190

Prime factors of 74190 are 2, 3, 5, 2473. Prime factorization of 74190 in exponential form is:

74190 = 2¹ × 3¹ × 5¹ × 2473¹

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 74190

List of positive integer factors of 74190 that divides 74190 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 2473, 4946, 7419, 12365, 14838, 24730, 37095

Step-4: Factors of 74200

List of positive integer factors of 74200 that divides 74190 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 74190 and 74200. The biggest common factor number is the GCF number.
So the greatest common factor 74190 and 74200 is 10.

Also check out the Least Common Multiple of 74190 and 74200