What is the Greatest Common Factor of 21189 and 21196?

Greatest common factor (GCF) of 21189 and 21196 is 7.

GCF(21189,21196) = 7

We will now calculate the prime factors of 21189 and 21196, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21189 and 21196.

How to find the GCF of 21189 and 21196?

We will first find the prime factorization of 21189 and 21196. After we will calculate the factors of 21189 and 21196 and find the biggest common factor number .

Step-1: Prime Factorization of 21189

Prime factors of 21189 are 3, 7, 1009. Prime factorization of 21189 in exponential form is:

21189 = 3¹ × 7¹ × 1009¹

Step-2: Prime Factorization of 21196

Prime factors of 21196 are 2, 7, 757. Prime factorization of 21196 in exponential form is:

21196 = 2² × 7¹ × 757¹

Step-3: Factors of 21189

List of positive integer factors of 21189 that divides 21189 without a remainder.

1, 3, 7, 21, 1009, 3027, 7063

Step-4: Factors of 21196

List of positive integer factors of 21196 that divides 21189 without a remainder.

1, 2, 4, 7, 14, 28, 757, 1514, 3028, 5299, 10598

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21189 and 21196. The biggest common factor number is the GCF number.
So the greatest common factor 21189 and 21196 is 7.

Also check out the Least Common Multiple of 21189 and 21196