What is the Greatest Common Factor of 20300 and 20314?

Greatest common factor (GCF) of 20300 and 20314 is 14.

GCF(20300,20314) = 14

We will now calculate the prime factors of 20300 and 20314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20300 and 20314.

How to find the GCF of 20300 and 20314?

We will first find the prime factorization of 20300 and 20314. After we will calculate the factors of 20300 and 20314 and find the biggest common factor number .

Step-1: Prime Factorization of 20300

Prime factors of 20300 are 2, 5, 7, 29. Prime factorization of 20300 in exponential form is:

20300 = 2² × 5² × 7¹ × 29¹

Step-2: Prime Factorization of 20314

Prime factors of 20314 are 2, 7, 1451. Prime factorization of 20314 in exponential form is:

20314 = 2¹ × 7¹ × 1451¹

Step-3: Factors of 20300

List of positive integer factors of 20300 that divides 20300 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 29, 35, 50, 58, 70, 100, 116, 140, 145, 175, 203, 290, 350, 406, 580, 700, 725, 812, 1015, 1450, 2030, 2900, 4060, 5075, 10150

Step-4: Factors of 20314

List of positive integer factors of 20314 that divides 20300 without a remainder.

1, 2, 7, 14, 1451, 2902, 10157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20300 and 20314. The biggest common factor number is the GCF number.
So the greatest common factor 20300 and 20314 is 14.

Also check out the Least Common Multiple of 20300 and 20314