What is the Greatest Common Factor of 29904 and 29919?

Greatest common factor (GCF) of 29904 and 29919 is 3.

GCF(29904,29919) = 3

We will now calculate the prime factors of 29904 and 29919, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29904 and 29919.

How to find the GCF of 29904 and 29919?

We will first find the prime factorization of 29904 and 29919. After we will calculate the factors of 29904 and 29919 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 29919

Prime factors of 29919 are 3, 9973. Prime factorization of 29919 in exponential form is:

29919 = 3¹ × 9973¹

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 29919

List of positive integer factors of 29919 that divides 29904 without a remainder.

1, 3, 9973

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29904 and 29919. The biggest common factor number is the GCF number.
So the greatest common factor 29904 and 29919 is 3.

Also check out the Least Common Multiple of 29904 and 29919