What is the Greatest Common Factor of 21714 and 21729?

Greatest common factor (GCF) of 21714 and 21729 is 3.

GCF(21714,21729) = 3

We will now calculate the prime factors of 21714 and 21729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21714 and 21729.

How to find the GCF of 21714 and 21729?

We will first find the prime factorization of 21714 and 21729. After we will calculate the factors of 21714 and 21729 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21729

Prime factors of 21729 are 3, 7243. Prime factorization of 21729 in exponential form is:

21729 = 3¹ × 7243¹

Step-3: Factors of 21714

List of positive integer factors of 21714 that divides 21714 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

Step-4: Factors of 21729

List of positive integer factors of 21729 that divides 21714 without a remainder.

1, 3, 7243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21714 and 21729. The biggest common factor number is the GCF number.
So the greatest common factor 21714 and 21729 is 3.

Also check out the Least Common Multiple of 21714 and 21729