What is the Greatest Common Factor of 21742 and 21756?

Greatest common factor (GCF) of 21742 and 21756 is 14.

GCF(21742,21756) = 14

We will now calculate the prime factors of 21742 and 21756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21742 and 21756.

How to find the GCF of 21742 and 21756?

We will first find the prime factorization of 21742 and 21756. After we will calculate the factors of 21742 and 21756 and find the biggest common factor number .

Step-1: Prime Factorization of 21742

Prime factors of 21742 are 2, 7, 1553. Prime factorization of 21742 in exponential form is:

21742 = 2¹ × 7¹ × 1553¹

Step-2: 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-3: Factors of 21742

List of positive integer factors of 21742 that divides 21742 without a remainder.

1, 2, 7, 14, 1553, 3106, 10871

Step-4: Factors of 21756

List of positive integer factors of 21756 that divides 21742 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21742 and 21756. The biggest common factor number is the GCF number.
So the greatest common factor 21742 and 21756 is 14.

Also check out the Least Common Multiple of 21742 and 21756