What is the Greatest Common Factor of 83200 and 83214?

Greatest common factor (GCF) of 83200 and 83214 is 2.

GCF(83200,83214) = 2

We will now calculate the prime factors of 83200 and 83214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83200 and 83214.

How to find the GCF of 83200 and 83214?

We will first find the prime factorization of 83200 and 83214. After we will calculate the factors of 83200 and 83214 and find the biggest common factor number .

Step-1: Prime Factorization of 83200

Prime factors of 83200 are 2, 5, 13. Prime factorization of 83200 in exponential form is:

83200 = 2⁸ × 5² × 13¹

Step-2: Prime Factorization of 83214

Prime factors of 83214 are 2, 3, 23, 67. Prime factorization of 83214 in exponential form is:

83214 = 2¹ × 3³ × 23¹ × 67¹

Step-3: Factors of 83200

List of positive integer factors of 83200 that divides 83200 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64, 65, 80, 100, 104, 128, 130, 160, 200, 208, 256, 260, 320, 325, 400, 416, 520, 640, 650, 800, 832, 1040, 1280, 1300, 1600, 1664, 2080, 2600, 3200, 3328, 4160, 5200, 6400, 8320, 10400, 16640, 20800, 41600

Step-4: Factors of 83214

List of positive integer factors of 83214 that divides 83200 without a remainder.

1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 67, 69, 134, 138, 201, 207, 402, 414, 603, 621, 1206, 1242, 1541, 1809, 3082, 3618, 4623, 9246, 13869, 27738, 41607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83200 and 83214. The biggest common factor number is the GCF number.
So the greatest common factor 83200 and 83214 is 2.

Also check out the Least Common Multiple of 83200 and 83214