What is the Greatest Common Factor of 21658 and 21672?

Greatest common factor (GCF) of 21658 and 21672 is 14.

GCF(21658,21672) = 14

We will now calculate the prime factors of 21658 and 21672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21658 and 21672.

How to find the GCF of 21658 and 21672?

We will first find the prime factorization of 21658 and 21672. After we will calculate the factors of 21658 and 21672 and find the biggest common factor number .

Step-1: Prime Factorization of 21658

Prime factors of 21658 are 2, 7, 13, 17. Prime factorization of 21658 in exponential form is:

21658 = 2¹ × 7² × 13¹ × 17¹

Step-2: Prime Factorization of 21672

Prime factors of 21672 are 2, 3, 7, 43. Prime factorization of 21672 in exponential form is:

21672 = 2³ × 3² × 7¹ × 43¹

Step-3: Factors of 21658

List of positive integer factors of 21658 that divides 21658 without a remainder.

1, 2, 7, 13, 14, 17, 26, 34, 49, 91, 98, 119, 182, 221, 238, 442, 637, 833, 1274, 1547, 1666, 3094, 10829

Step-4: Factors of 21672

List of positive integer factors of 21672 that divides 21658 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 43, 56, 63, 72, 84, 86, 126, 129, 168, 172, 252, 258, 301, 344, 387, 504, 516, 602, 774, 903, 1032, 1204, 1548, 1806, 2408, 2709, 3096, 3612, 5418, 7224, 10836

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21658 and 21672. The biggest common factor number is the GCF number.
So the greatest common factor 21658 and 21672 is 14.

Also check out the Least Common Multiple of 21658 and 21672