What is the Greatest Common Factor of 21756 and 21770?

Greatest common factor (GCF) of 21756 and 21770 is 14.

GCF(21756,21770) = 14

We will now calculate the prime factors of 21756 and 21770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21756 and 21770.

How to find the GCF of 21756 and 21770?

We will first find the prime factorization of 21756 and 21770. After we will calculate the factors of 21756 and 21770 and find the biggest common factor number .

Step-1: Prime Factorization of 21756

Prime factors of 21756 are 2, 3, 7, 37. Prime factorization of 21756 in exponential form is:

21756 = 2² × 3¹ × 7² × 37¹

Step-2: Prime Factorization of 21770

Prime factors of 21770 are 2, 5, 7, 311. Prime factorization of 21770 in exponential form is:

21770 = 2¹ × 5¹ × 7¹ × 311¹

Step-3: Factors of 21756

List of positive integer factors of 21756 that divides 21756 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 37, 42, 49, 74, 84, 98, 111, 147, 148, 196, 222, 259, 294, 444, 518, 588, 777, 1036, 1554, 1813, 3108, 3626, 5439, 7252, 10878

Step-4: Factors of 21770

List of positive integer factors of 21770 that divides 21756 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 311, 622, 1555, 2177, 3110, 4354, 10885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21756 and 21770. The biggest common factor number is the GCF number.
So the greatest common factor 21756 and 21770 is 14.

Also check out the Least Common Multiple of 21756 and 21770