What is the Greatest Common Factor of 39200 and 39216?

Greatest common factor (GCF) of 39200 and 39216 is 16.

GCF(39200,39216) = 16

We will now calculate the prime factors of 39200 and 39216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39200 and 39216.

How to find the GCF of 39200 and 39216?

We will first find the prime factorization of 39200 and 39216. After we will calculate the factors of 39200 and 39216 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39216

Prime factors of 39216 are 2, 3, 19, 43. Prime factorization of 39216 in exponential form is:

39216 = 2⁴ × 3¹ × 19¹ × 43¹

Step-3: Factors of 39200

List of positive integer factors of 39200 that divides 39200 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

Step-4: Factors of 39216

List of positive integer factors of 39216 that divides 39200 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 43, 48, 57, 76, 86, 114, 129, 152, 172, 228, 258, 304, 344, 456, 516, 688, 817, 912, 1032, 1634, 2064, 2451, 3268, 4902, 6536, 9804, 13072, 19608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39200 and 39216. The biggest common factor number is the GCF number.
So the greatest common factor 39200 and 39216 is 16.

Also check out the Least Common Multiple of 39200 and 39216