What is the Greatest Common Factor of 21696 and 21708?

Greatest common factor (GCF) of 21696 and 21708 is 12.

GCF(21696,21708) = 12

We will now calculate the prime factors of 21696 and 21708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21696 and 21708.

How to find the GCF of 21696 and 21708?

We will first find the prime factorization of 21696 and 21708. After we will calculate the factors of 21696 and 21708 and find the biggest common factor number .

Step-1: Prime Factorization of 21696

Prime factors of 21696 are 2, 3, 113. Prime factorization of 21696 in exponential form is:

21696 = 2⁶ × 3¹ × 113¹

Step-2: Prime Factorization of 21708

Prime factors of 21708 are 2, 3, 67. Prime factorization of 21708 in exponential form is:

21708 = 2² × 3⁴ × 67¹

Step-3: Factors of 21696

List of positive integer factors of 21696 that divides 21696 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 113, 192, 226, 339, 452, 678, 904, 1356, 1808, 2712, 3616, 5424, 7232, 10848

Step-4: Factors of 21708

List of positive integer factors of 21708 that divides 21696 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 67, 81, 108, 134, 162, 201, 268, 324, 402, 603, 804, 1206, 1809, 2412, 3618, 5427, 7236, 10854

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21696 and 21708. The biggest common factor number is the GCF number.
So the greatest common factor 21696 and 21708 is 12.

Also check out the Least Common Multiple of 21696 and 21708