What is the Greatest Common Factor of 21300 and 21307?

Greatest common factor (GCF) of 21300 and 21307 is 1.

GCF(21300,21307) = 1

We will now calculate the prime factors of 21300 and 21307, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21300 and 21307.

How to find the GCF of 21300 and 21307?

We will first find the prime factorization of 21300 and 21307. After we will calculate the factors of 21300 and 21307 and find the biggest common factor number .

Step-1: Prime Factorization of 21300

Prime factors of 21300 are 2, 3, 5, 71. Prime factorization of 21300 in exponential form is:

21300 = 2² × 3¹ × 5² × 71¹

Step-2: Prime Factorization of 21307

Prime factors of 21307 are 11, 13, 149. Prime factorization of 21307 in exponential form is:

21307 = 11¹ × 13¹ × 149¹

Step-3: Factors of 21300

List of positive integer factors of 21300 that divides 21300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 71, 75, 100, 142, 150, 213, 284, 300, 355, 426, 710, 852, 1065, 1420, 1775, 2130, 3550, 4260, 5325, 7100, 10650

Step-4: Factors of 21307

List of positive integer factors of 21307 that divides 21300 without a remainder.

1, 11, 13, 143, 149, 1639, 1937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21300 and 21307. The biggest common factor number is the GCF number.
So the greatest common factor 21300 and 21307 is 1.

Also check out the Least Common Multiple of 21300 and 21307