What is the Greatest Common Factor of 39180 and 39200?

Greatest common factor (GCF) of 39180 and 39200 is 20.

GCF(39180,39200) = 20

We will now calculate the prime factors of 39180 and 39200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39180 and 39200.

How to find the GCF of 39180 and 39200?

We will first find the prime factorization of 39180 and 39200. After we will calculate the factors of 39180 and 39200 and find the biggest common factor number .

Step-1: Prime Factorization of 39180

Prime factors of 39180 are 2, 3, 5, 653. Prime factorization of 39180 in exponential form is:

39180 = 2² × 3¹ × 5¹ × 653¹

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 39180

List of positive integer factors of 39180 that divides 39180 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 653, 1306, 1959, 2612, 3265, 3918, 6530, 7836, 9795, 13060, 19590

Step-4: Factors of 39200

List of positive integer factors of 39200 that divides 39180 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 39180 and 39200. The biggest common factor number is the GCF number.
So the greatest common factor 39180 and 39200 is 20.

Also check out the Least Common Multiple of 39180 and 39200