What is the Greatest Common Factor of 21680 and 21690?

Greatest common factor (GCF) of 21680 and 21690 is 10.

GCF(21680,21690) = 10

We will now calculate the prime factors of 21680 and 21690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21680 and 21690.

How to find the GCF of 21680 and 21690?

We will first find the prime factorization of 21680 and 21690. After we will calculate the factors of 21680 and 21690 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 21690

Prime factors of 21690 are 2, 3, 5, 241. Prime factorization of 21690 in exponential form is:

21690 = 2¹ × 3² × 5¹ × 241¹

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 21690

List of positive integer factors of 21690 that divides 21680 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 241, 482, 723, 1205, 1446, 2169, 2410, 3615, 4338, 7230, 10845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21680 and 21690. The biggest common factor number is the GCF number.
So the greatest common factor 21680 and 21690 is 10.

Also check out the Least Common Multiple of 21680 and 21690