What is the Greatest Common Factor of 39200 and 39214?

Greatest common factor (GCF) of 39200 and 39214 is 14.

GCF(39200,39214) = 14

We will now calculate the prime factors of 39200 and 39214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39200 and 39214.

How to find the GCF of 39200 and 39214?

We will first find the prime factorization of 39200 and 39214. After we will calculate the factors of 39200 and 39214 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 39214

Prime factors of 39214 are 2, 7, 2801. Prime factorization of 39214 in exponential form is:

39214 = 2¹ × 7¹ × 2801¹

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 39214

List of positive integer factors of 39214 that divides 39200 without a remainder.

1, 2, 7, 14, 2801, 5602, 19607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39200 and 39214. The biggest common factor number is the GCF number.
So the greatest common factor 39200 and 39214 is 14.

Also check out the Least Common Multiple of 39200 and 39214