What is the Greatest Common Factor of 21686 and 21700?

Greatest common factor (GCF) of 21686 and 21700 is 14.

GCF(21686,21700) = 14

We will now calculate the prime factors of 21686 and 21700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21686 and 21700.

How to find the GCF of 21686 and 21700?

We will first find the prime factorization of 21686 and 21700. After we will calculate the factors of 21686 and 21700 and find the biggest common factor number .

Step-1: Prime Factorization of 21686

Prime factors of 21686 are 2, 7, 1549. Prime factorization of 21686 in exponential form is:

21686 = 2¹ × 7¹ × 1549¹

Step-2: Prime Factorization of 21700

Prime factors of 21700 are 2, 5, 7, 31. Prime factorization of 21700 in exponential form is:

21700 = 2² × 5² × 7¹ × 31¹

Step-3: Factors of 21686

List of positive integer factors of 21686 that divides 21686 without a remainder.

1, 2, 7, 14, 1549, 3098, 10843

Step-4: Factors of 21700

List of positive integer factors of 21700 that divides 21686 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 31, 35, 50, 62, 70, 100, 124, 140, 155, 175, 217, 310, 350, 434, 620, 700, 775, 868, 1085, 1550, 2170, 3100, 4340, 5425, 10850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21686 and 21700. The biggest common factor number is the GCF number.
So the greatest common factor 21686 and 21700 is 14.

Also check out the Least Common Multiple of 21686 and 21700