What is the Greatest Common Factor of 74200 and 74208?

Greatest common factor (GCF) of 74200 and 74208 is 8.

GCF(74200,74208) = 8

We will now calculate the prime factors of 74200 and 74208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74200 and 74208.

How to find the GCF of 74200 and 74208?

We will first find the prime factorization of 74200 and 74208. After we will calculate the factors of 74200 and 74208 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 74208

Prime factors of 74208 are 2, 3, 773. Prime factorization of 74208 in exponential form is:

74208 = 2⁵ × 3¹ × 773¹

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 74208

List of positive integer factors of 74208 that divides 74200 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 773, 1546, 2319, 3092, 4638, 6184, 9276, 12368, 18552, 24736, 37104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74200 and 74208. The biggest common factor number is the GCF number.
So the greatest common factor 74200 and 74208 is 8.

Also check out the Least Common Multiple of 74200 and 74208