What is the Greatest Common Factor of 38496 and 38509?

Greatest common factor (GCF) of 38496 and 38509 is 1.

GCF(38496,38509) = 1

We will now calculate the prime factors of 38496 and 38509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38496 and 38509.

How to find the GCF of 38496 and 38509?

We will first find the prime factorization of 38496 and 38509. After we will calculate the factors of 38496 and 38509 and find the biggest common factor number .

Step-1: Prime Factorization of 38496

Prime factors of 38496 are 2, 3, 401. Prime factorization of 38496 in exponential form is:

38496 = 2⁵ × 3¹ × 401¹

Step-2: Prime Factorization of 38509

Prime factors of 38509 are 97, 397. Prime factorization of 38509 in exponential form is:

38509 = 97¹ × 397¹

Step-3: Factors of 38496

List of positive integer factors of 38496 that divides 38496 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 401, 802, 1203, 1604, 2406, 3208, 4812, 6416, 9624, 12832, 19248

Step-4: Factors of 38509

List of positive integer factors of 38509 that divides 38496 without a remainder.

1, 97, 397

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38496 and 38509. The biggest common factor number is the GCF number.
So the greatest common factor 38496 and 38509 is 1.

Also check out the Least Common Multiple of 38496 and 38509