What is the Greatest Common Factor of 34300 and 34314?

Greatest common factor (GCF) of 34300 and 34314 is 14.

GCF(34300,34314) = 14

We will now calculate the prime factors of 34300 and 34314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34300 and 34314.

How to find the GCF of 34300 and 34314?

We will first find the prime factorization of 34300 and 34314. After we will calculate the factors of 34300 and 34314 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34314

Prime factors of 34314 are 2, 3, 7, 19, 43. Prime factorization of 34314 in exponential form is:

34314 = 2¹ × 3¹ × 7¹ × 19¹ × 43¹

Step-3: Factors of 34300

List of positive integer factors of 34300 that divides 34300 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

Step-4: Factors of 34314

List of positive integer factors of 34314 that divides 34300 without a remainder.

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 43, 57, 86, 114, 129, 133, 258, 266, 301, 399, 602, 798, 817, 903, 1634, 1806, 2451, 4902, 5719, 11438, 17157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34300 and 34314. The biggest common factor number is the GCF number.
So the greatest common factor 34300 and 34314 is 14.

Also check out the Least Common Multiple of 34300 and 34314