What is the Greatest Common Factor of 83214 and 83232?

Greatest common factor (GCF) of 83214 and 83232 is 18.

GCF(83214,83232) = 18

We will now calculate the prime factors of 83214 and 83232, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83214 and 83232.

How to find the GCF of 83214 and 83232?

We will first find the prime factorization of 83214 and 83232. After we will calculate the factors of 83214 and 83232 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 83232

Prime factors of 83232 are 2, 3, 17. Prime factorization of 83232 in exponential form is:

83232 = 2⁵ × 3² × 17²

Step-3: Factors of 83214

List of positive integer factors of 83214 that divides 83214 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

Step-4: Factors of 83232

List of positive integer factors of 83232 that divides 83214 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 68, 72, 96, 102, 136, 144, 153, 204, 272, 288, 289, 306, 408, 544, 578, 612, 816, 867, 1156, 1224, 1632, 1734, 2312, 2448, 2601, 3468, 4624, 4896, 5202, 6936, 9248, 10404, 13872, 20808, 27744, 41616

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83214 and 83232. The biggest common factor number is the GCF number.
So the greatest common factor 83214 and 83232 is 18.

Also check out the Least Common Multiple of 83214 and 83232