What is the Greatest Common Factor of 74208 and 74223?

Greatest common factor (GCF) of 74208 and 74223 is 3.

GCF(74208,74223) = 3

We will now calculate the prime factors of 74208 and 74223, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74208 and 74223.

How to find the GCF of 74208 and 74223?

We will first find the prime factorization of 74208 and 74223. After we will calculate the factors of 74208 and 74223 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 74223

Prime factors of 74223 are 3, 2749. Prime factorization of 74223 in exponential form is:

74223 = 3³ × 2749¹

Step-3: Factors of 74208

List of positive integer factors of 74208 that divides 74208 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

Step-4: Factors of 74223

List of positive integer factors of 74223 that divides 74208 without a remainder.

1, 3, 9, 27, 2749, 8247, 24741

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74208 and 74223. The biggest common factor number is the GCF number.
So the greatest common factor 74208 and 74223 is 3.

Also check out the Least Common Multiple of 74208 and 74223