What is the Greatest Common Factor of 21762 and 21776?

Greatest common factor (GCF) of 21762 and 21776 is 2.

GCF(21762,21776) = 2

We will now calculate the prime factors of 21762 and 21776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21762 and 21776.

How to find the GCF of 21762 and 21776?

We will first find the prime factorization of 21762 and 21776. After we will calculate the factors of 21762 and 21776 and find the biggest common factor number .

Step-1: Prime Factorization of 21762

Prime factors of 21762 are 2, 3, 13, 31. Prime factorization of 21762 in exponential form is:

21762 = 2¹ × 3³ × 13¹ × 31¹

Step-2: Prime Factorization of 21776

Prime factors of 21776 are 2, 1361. Prime factorization of 21776 in exponential form is:

21776 = 2⁴ × 1361¹

Step-3: Factors of 21762

List of positive integer factors of 21762 that divides 21762 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 31, 39, 54, 62, 78, 93, 117, 186, 234, 279, 351, 403, 558, 702, 806, 837, 1209, 1674, 2418, 3627, 7254, 10881

Step-4: Factors of 21776

List of positive integer factors of 21776 that divides 21762 without a remainder.

1, 2, 4, 8, 16, 1361, 2722, 5444, 10888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21762 and 21776. The biggest common factor number is the GCF number.
So the greatest common factor 21762 and 21776 is 2.

Also check out the Least Common Multiple of 21762 and 21776