What is the Greatest Common Factor of 74188 and 74208?

Greatest common factor (GCF) of 74188 and 74208 is 4.

GCF(74188,74208) = 4

We will now calculate the prime factors of 74188 and 74208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74188 and 74208.

How to find the GCF of 74188 and 74208?

We will first find the prime factorization of 74188 and 74208. After we will calculate the factors of 74188 and 74208 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 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 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 74208

List of positive integer factors of 74208 that divides 74188 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 74188 and 74208. The biggest common factor number is the GCF number.
So the greatest common factor 74188 and 74208 is 4.

Also check out the Least Common Multiple of 74188 and 74208