What is the Greatest Common Factor of 39188 and 39200?

Greatest common factor (GCF) of 39188 and 39200 is 4.

GCF(39188,39200) = 4

We will now calculate the prime factors of 39188 and 39200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39188 and 39200.

How to find the GCF of 39188 and 39200?

We will first find the prime factorization of 39188 and 39200. After we will calculate the factors of 39188 and 39200 and find the biggest common factor number .

Step-1: Prime Factorization of 39188

Prime factors of 39188 are 2, 97, 101. Prime factorization of 39188 in exponential form is:

39188 = 2² × 97¹ × 101¹

Step-2: Prime Factorization of 39200

Prime factors of 39200 are 2, 5, 7. Prime factorization of 39200 in exponential form is:

39200 = 2⁵ × 5² × 7²

Step-3: Factors of 39188

List of positive integer factors of 39188 that divides 39188 without a remainder.

1, 2, 4, 97, 101, 194, 202, 388, 404, 9797, 19594

Step-4: Factors of 39200

List of positive integer factors of 39200 that divides 39188 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49, 50, 56, 70, 80, 98, 100, 112, 140, 160, 175, 196, 200, 224, 245, 280, 350, 392, 400, 490, 560, 700, 784, 800, 980, 1120, 1225, 1400, 1568, 1960, 2450, 2800, 3920, 4900, 5600, 7840, 9800, 19600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39188 and 39200. The biggest common factor number is the GCF number.
So the greatest common factor 39188 and 39200 is 4.

Also check out the Least Common Multiple of 39188 and 39200