What is the Greatest Common Factor of 20904 and 20916?

Greatest common factor (GCF) of 20904 and 20916 is 12.

GCF(20904,20916) = 12

We will now calculate the prime factors of 20904 and 20916, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20904 and 20916.

How to find the GCF of 20904 and 20916?

We will first find the prime factorization of 20904 and 20916. After we will calculate the factors of 20904 and 20916 and find the biggest common factor number .

Step-1: Prime Factorization of 20904

Prime factors of 20904 are 2, 3, 13, 67. Prime factorization of 20904 in exponential form is:

20904 = 2³ × 3¹ × 13¹ × 67¹

Step-2: Prime Factorization of 20916

Prime factors of 20916 are 2, 3, 7, 83. Prime factorization of 20916 in exponential form is:

20916 = 2² × 3² × 7¹ × 83¹

Step-3: Factors of 20904

List of positive integer factors of 20904 that divides 20904 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 67, 78, 104, 134, 156, 201, 268, 312, 402, 536, 804, 871, 1608, 1742, 2613, 3484, 5226, 6968, 10452

Step-4: Factors of 20916

List of positive integer factors of 20916 that divides 20904 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 83, 84, 126, 166, 249, 252, 332, 498, 581, 747, 996, 1162, 1494, 1743, 2324, 2988, 3486, 5229, 6972, 10458

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20904 and 20916. The biggest common factor number is the GCF number.
So the greatest common factor 20904 and 20916 is 12.

Also check out the Least Common Multiple of 20904 and 20916