What is the Greatest Common Factor of 29904 and 29916?

Greatest common factor (GCF) of 29904 and 29916 is 12.

GCF(29904,29916) = 12

We will now calculate the prime factors of 29904 and 29916, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29904 and 29916.

How to find the GCF of 29904 and 29916?

We will first find the prime factorization of 29904 and 29916. After we will calculate the factors of 29904 and 29916 and find the biggest common factor number .

Step-1: Prime Factorization of 29904

Prime factors of 29904 are 2, 3, 7, 89. Prime factorization of 29904 in exponential form is:

29904 = 2⁴ × 3¹ × 7¹ × 89¹

Step-2: Prime Factorization of 29916

Prime factors of 29916 are 2, 3, 277. Prime factorization of 29916 in exponential form is:

29916 = 2² × 3³ × 277¹

Step-3: Factors of 29904

List of positive integer factors of 29904 that divides 29904 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 89, 112, 168, 178, 267, 336, 356, 534, 623, 712, 1068, 1246, 1424, 1869, 2136, 2492, 3738, 4272, 4984, 7476, 9968, 14952

Step-4: Factors of 29916

List of positive integer factors of 29916 that divides 29904 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 7479, 9972, 14958

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29904 and 29916. The biggest common factor number is the GCF number.
So the greatest common factor 29904 and 29916 is 12.

Also check out the Least Common Multiple of 29904 and 29916