What is the Greatest Common Factor of 86208 and 86214?

Greatest common factor (GCF) of 86208 and 86214 is 6.

GCF(86208,86214) = 6

We will now calculate the prime factors of 86208 and 86214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 86208 and 86214.

How to find the GCF of 86208 and 86214?

We will first find the prime factorization of 86208 and 86214. After we will calculate the factors of 86208 and 86214 and find the biggest common factor number .

Step-1: Prime Factorization of 86208

Prime factors of 86208 are 2, 3, 449. Prime factorization of 86208 in exponential form is:

86208 = 2⁶ × 3¹ × 449¹

Step-2: Prime Factorization of 86214

Prime factors of 86214 are 2, 3, 14369. Prime factorization of 86214 in exponential form is:

86214 = 2¹ × 3¹ × 14369¹

Step-3: Factors of 86208

List of positive integer factors of 86208 that divides 86208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 449, 898, 1347, 1796, 2694, 3592, 5388, 7184, 10776, 14368, 21552, 28736, 43104

Step-4: Factors of 86214

List of positive integer factors of 86214 that divides 86208 without a remainder.

1, 2, 3, 6, 14369, 28738, 43107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 86208 and 86214. The biggest common factor number is the GCF number.
So the greatest common factor 86208 and 86214 is 6.

Also check out the Least Common Multiple of 86208 and 86214