What is the Greatest Common Factor of 21614 and 21632?

Greatest common factor (GCF) of 21614 and 21632 is 2.

GCF(21614,21632) = 2

We will now calculate the prime factors of 21614 and 21632, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21614 and 21632.

How to find the GCF of 21614 and 21632?

We will first find the prime factorization of 21614 and 21632. After we will calculate the factors of 21614 and 21632 and find the biggest common factor number .

Step-1: Prime Factorization of 21614

Prime factors of 21614 are 2, 101, 107. Prime factorization of 21614 in exponential form is:

21614 = 2¹ × 101¹ × 107¹

Step-2: Prime Factorization of 21632

Prime factors of 21632 are 2, 13. Prime factorization of 21632 in exponential form is:

21632 = 2⁷ × 13²

Step-3: Factors of 21614

List of positive integer factors of 21614 that divides 21614 without a remainder.

1, 2, 101, 107, 202, 214, 10807

Step-4: Factors of 21632

List of positive integer factors of 21632 that divides 21614 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 169, 208, 338, 416, 676, 832, 1352, 1664, 2704, 5408, 10816

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21614 and 21632. The biggest common factor number is the GCF number.
So the greatest common factor 21614 and 21632 is 2.

Also check out the Least Common Multiple of 21614 and 21632