What is the Greatest Common Factor of 32200 and 32214?

Greatest common factor (GCF) of 32200 and 32214 is 14.

GCF(32200,32214) = 14

We will now calculate the prime factors of 32200 and 32214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32200 and 32214.

How to find the GCF of 32200 and 32214?

We will first find the prime factorization of 32200 and 32214. After we will calculate the factors of 32200 and 32214 and find the biggest common factor number .

Step-1: Prime Factorization of 32200

Prime factors of 32200 are 2, 5, 7, 23. Prime factorization of 32200 in exponential form is:

32200 = 2³ × 5² × 7¹ × 23¹

Step-2: Prime Factorization of 32214

Prime factors of 32214 are 2, 3, 7, 13, 59. Prime factorization of 32214 in exponential form is:

32214 = 2¹ × 3¹ × 7¹ × 13¹ × 59¹

Step-3: Factors of 32200

List of positive integer factors of 32200 that divides 32200 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 23, 25, 28, 35, 40, 46, 50, 56, 70, 92, 100, 115, 140, 161, 175, 184, 200, 230, 280, 322, 350, 460, 575, 644, 700, 805, 920, 1150, 1288, 1400, 1610, 2300, 3220, 4025, 4600, 6440, 8050, 16100

Step-4: Factors of 32214

List of positive integer factors of 32214 that divides 32200 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 59, 78, 91, 118, 177, 182, 273, 354, 413, 546, 767, 826, 1239, 1534, 2301, 2478, 4602, 5369, 10738, 16107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32200 and 32214. The biggest common factor number is the GCF number.
So the greatest common factor 32200 and 32214 is 14.

Also check out the Least Common Multiple of 32200 and 32214