What is the Greatest Common Factor of 21680 and 21686?

Greatest common factor (GCF) of 21680 and 21686 is 2.

GCF(21680,21686) = 2

We will now calculate the prime factors of 21680 and 21686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21680 and 21686.

How to find the GCF of 21680 and 21686?

We will first find the prime factorization of 21680 and 21686. After we will calculate the factors of 21680 and 21686 and find the biggest common factor number .

Step-1: Prime Factorization of 21680

Prime factors of 21680 are 2, 5, 271. Prime factorization of 21680 in exponential form is:

21680 = 2⁴ × 5¹ × 271¹

Step-2: Prime Factorization of 21686

Prime factors of 21686 are 2, 7, 1549. Prime factorization of 21686 in exponential form is:

21686 = 2¹ × 7¹ × 1549¹

Step-3: Factors of 21680

List of positive integer factors of 21680 that divides 21680 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 271, 542, 1084, 1355, 2168, 2710, 4336, 5420, 10840

Step-4: Factors of 21686

List of positive integer factors of 21686 that divides 21680 without a remainder.

1, 2, 7, 14, 1549, 3098, 10843

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21680 and 21686. The biggest common factor number is the GCF number.
So the greatest common factor 21680 and 21686 is 2.

Also check out the Least Common Multiple of 21680 and 21686