What is the Greatest Common Factor of 21691 and 21700?

Greatest common factor (GCF) of 21691 and 21700 is 1.

GCF(21691,21700) = 1

We will now calculate the prime factors of 21691 and 21700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21691 and 21700.

How to find the GCF of 21691 and 21700?

We will first find the prime factorization of 21691 and 21700. After we will calculate the factors of 21691 and 21700 and find the biggest common factor number .

Step-1: Prime Factorization of 21691

Prime factors of 21691 are 109, 199. Prime factorization of 21691 in exponential form is:

21691 = 109¹ × 199¹

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 21691

List of positive integer factors of 21691 that divides 21691 without a remainder.

1, 109, 199

Step-4: Factors of 21700

List of positive integer factors of 21700 that divides 21691 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 21691 and 21700. The biggest common factor number is the GCF number.
So the greatest common factor 21691 and 21700 is 1.

Also check out the Least Common Multiple of 21691 and 21700