What is the Greatest Common Factor of 20286 and 20300?

Greatest common factor (GCF) of 20286 and 20300 is 14.

GCF(20286,20300) = 14

We will now calculate the prime factors of 20286 and 20300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20286 and 20300.

How to find the GCF of 20286 and 20300?

We will first find the prime factorization of 20286 and 20300. After we will calculate the factors of 20286 and 20300 and find the biggest common factor number .

Step-1: Prime Factorization of 20286

Prime factors of 20286 are 2, 3, 7, 23. Prime factorization of 20286 in exponential form is:

20286 = 2¹ × 3² × 7² × 23¹

Step-2: 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-3: Factors of 20286

List of positive integer factors of 20286 that divides 20286 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 23, 42, 46, 49, 63, 69, 98, 126, 138, 147, 161, 207, 294, 322, 414, 441, 483, 882, 966, 1127, 1449, 2254, 2898, 3381, 6762, 10143

Step-4: Factors of 20300

List of positive integer factors of 20300 that divides 20286 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20286 and 20300. The biggest common factor number is the GCF number.
So the greatest common factor 20286 and 20300 is 14.

Also check out the Least Common Multiple of 20286 and 20300