What is the Greatest Common Factor of 21705 and 21714?

Greatest common factor (GCF) of 21705 and 21714 is 3.

GCF(21705,21714) = 3

We will now calculate the prime factors of 21705 and 21714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21705 and 21714.

How to find the GCF of 21705 and 21714?

We will first find the prime factorization of 21705 and 21714. After we will calculate the factors of 21705 and 21714 and find the biggest common factor number .

Step-1: Prime Factorization of 21705

Prime factors of 21705 are 3, 5, 1447. Prime factorization of 21705 in exponential form is:

21705 = 3¹ × 5¹ × 1447¹

Step-2: Prime Factorization of 21714

Prime factors of 21714 are 2, 3, 7, 11, 47. Prime factorization of 21714 in exponential form is:

21714 = 2¹ × 3¹ × 7¹ × 11¹ × 47¹

Step-3: Factors of 21705

List of positive integer factors of 21705 that divides 21705 without a remainder.

1, 3, 5, 15, 1447, 4341, 7235

Step-4: Factors of 21714

List of positive integer factors of 21714 that divides 21705 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 47, 66, 77, 94, 141, 154, 231, 282, 329, 462, 517, 658, 987, 1034, 1551, 1974, 3102, 3619, 7238, 10857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21705 and 21714. The biggest common factor number is the GCF number.
So the greatest common factor 21705 and 21714 is 3.

Also check out the Least Common Multiple of 21705 and 21714