What is the Greatest Common Factor of 38402 and 38416?

Greatest common factor (GCF) of 38402 and 38416 is 14.

GCF(38402,38416) = 14

We will now calculate the prime factors of 38402 and 38416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38402 and 38416.

How to find the GCF of 38402 and 38416?

We will first find the prime factorization of 38402 and 38416. After we will calculate the factors of 38402 and 38416 and find the biggest common factor number .

Step-1: Prime Factorization of 38402

Prime factors of 38402 are 2, 7, 13, 211. Prime factorization of 38402 in exponential form is:

38402 = 2¹ × 7¹ × 13¹ × 211¹

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 38402

List of positive integer factors of 38402 that divides 38402 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 211, 422, 1477, 2743, 2954, 5486, 19201

Step-4: Factors of 38416

List of positive integer factors of 38416 that divides 38402 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 38402 and 38416. The biggest common factor number is the GCF number.
So the greatest common factor 38402 and 38416 is 14.

Also check out the Least Common Multiple of 38402 and 38416