What is the Greatest Common Factor of 38409 and 38416?

Greatest common factor (GCF) of 38409 and 38416 is 7.

GCF(38409,38416) = 7

We will now calculate the prime factors of 38409 and 38416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38409 and 38416.

How to find the GCF of 38409 and 38416?

We will first find the prime factorization of 38409 and 38416. After we will calculate the factors of 38409 and 38416 and find the biggest common factor number .

Step-1: Prime Factorization of 38409

Prime factors of 38409 are 3, 7, 31, 59. Prime factorization of 38409 in exponential form is:

38409 = 3¹ × 7¹ × 31¹ × 59¹

Step-2: Prime Factorization of 38416

Prime factors of 38416 are 2, 7. Prime factorization of 38416 in exponential form is:

38416 = 2⁴ × 7⁴

Step-3: Factors of 38409

List of positive integer factors of 38409 that divides 38409 without a remainder.

1, 3, 7, 21, 31, 59, 93, 177, 217, 413, 651, 1239, 1829, 5487, 12803

Step-4: Factors of 38416

List of positive integer factors of 38416 that divides 38409 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 343, 392, 686, 784, 1372, 2401, 2744, 4802, 5488, 9604, 19208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38409 and 38416. The biggest common factor number is the GCF number.
So the greatest common factor 38409 and 38416 is 7.

Also check out the Least Common Multiple of 38409 and 38416