What is the Greatest Common Factor of 21614 and 21630?

Greatest common factor (GCF) of 21614 and 21630 is 2.

GCF(21614,21630) = 2

We will now calculate the prime factors of 21614 and 21630, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21614 and 21630.

How to find the GCF of 21614 and 21630?

We will first find the prime factorization of 21614 and 21630. After we will calculate the factors of 21614 and 21630 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 21630

Prime factors of 21630 are 2, 3, 5, 7, 103. Prime factorization of 21630 in exponential form is:

21630 = 2¹ × 3¹ × 5¹ × 7¹ × 103¹

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 21630

List of positive integer factors of 21630 that divides 21614 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 103, 105, 206, 210, 309, 515, 618, 721, 1030, 1442, 1545, 2163, 3090, 3605, 4326, 7210, 10815

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21614 and 21630. The biggest common factor number is the GCF number.
So the greatest common factor 21614 and 21630 is 2.

Also check out the Least Common Multiple of 21614 and 21630