What is the Greatest Common Factor of 23300 and 23314?

Greatest common factor (GCF) of 23300 and 23314 is 2.

GCF(23300,23314) = 2

We will now calculate the prime factors of 23300 and 23314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23300 and 23314.

How to find the GCF of 23300 and 23314?

We will first find the prime factorization of 23300 and 23314. After we will calculate the factors of 23300 and 23314 and find the biggest common factor number .

Step-1: Prime Factorization of 23300

Prime factors of 23300 are 2, 5, 233. Prime factorization of 23300 in exponential form is:

23300 = 2² × 5² × 233¹

Step-2: Prime Factorization of 23314

Prime factors of 23314 are 2, 11657. Prime factorization of 23314 in exponential form is:

23314 = 2¹ × 11657¹

Step-3: Factors of 23300

List of positive integer factors of 23300 that divides 23300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 233, 466, 932, 1165, 2330, 4660, 5825, 11650

Step-4: Factors of 23314

List of positive integer factors of 23314 that divides 23300 without a remainder.

1, 2, 11657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23300 and 23314. The biggest common factor number is the GCF number.
So the greatest common factor 23300 and 23314 is 2.

Also check out the Least Common Multiple of 23300 and 23314