What is the Greatest Common Factor of 21196 and 21210?

Greatest common factor (GCF) of 21196 and 21210 is 14.

GCF(21196,21210) = 14

We will now calculate the prime factors of 21196 and 21210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21196 and 21210.

How to find the GCF of 21196 and 21210?

We will first find the prime factorization of 21196 and 21210. After we will calculate the factors of 21196 and 21210 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21210

Prime factors of 21210 are 2, 3, 5, 7, 101. Prime factorization of 21210 in exponential form is:

21210 = 2¹ × 3¹ × 5¹ × 7¹ × 101¹

Step-3: Factors of 21196

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

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

Step-4: Factors of 21210

List of positive integer factors of 21210 that divides 21196 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 101, 105, 202, 210, 303, 505, 606, 707, 1010, 1414, 1515, 2121, 3030, 3535, 4242, 7070, 10605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21196 and 21210. The biggest common factor number is the GCF number.
So the greatest common factor 21196 and 21210 is 14.

Also check out the Least Common Multiple of 21196 and 21210