What is the Greatest Common Factor of 34286 and 34300?

Greatest common factor (GCF) of 34286 and 34300 is 14.

GCF(34286,34300) = 14

We will now calculate the prime factors of 34286 and 34300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34286 and 34300.

How to find the GCF of 34286 and 34300?

We will first find the prime factorization of 34286 and 34300. After we will calculate the factors of 34286 and 34300 and find the biggest common factor number .

Step-1: Prime Factorization of 34286

Prime factors of 34286 are 2, 7, 31, 79. Prime factorization of 34286 in exponential form is:

34286 = 2¹ × 7¹ × 31¹ × 79¹

Step-2: Prime Factorization of 34300

Prime factors of 34300 are 2, 5, 7. Prime factorization of 34300 in exponential form is:

34300 = 2² × 5² × 7³

Step-3: Factors of 34286

List of positive integer factors of 34286 that divides 34286 without a remainder.

1, 2, 7, 14, 31, 62, 79, 158, 217, 434, 553, 1106, 2449, 4898, 17143

Step-4: Factors of 34300

List of positive integer factors of 34300 that divides 34286 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 343, 350, 490, 686, 700, 980, 1225, 1372, 1715, 2450, 3430, 4900, 6860, 8575, 17150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34286 and 34300. The biggest common factor number is the GCF number.
So the greatest common factor 34286 and 34300 is 14.

Also check out the Least Common Multiple of 34286 and 34300