What is the Greatest Common Factor of 29937 and 29952?

Greatest common factor (GCF) of 29937 and 29952 is 3.

GCF(29937,29952) = 3

We will now calculate the prime factors of 29937 and 29952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29937 and 29952.

How to find the GCF of 29937 and 29952?

We will first find the prime factorization of 29937 and 29952. After we will calculate the factors of 29937 and 29952 and find the biggest common factor number .

Step-1: Prime Factorization of 29937

Prime factors of 29937 are 3, 17, 587. Prime factorization of 29937 in exponential form is:

29937 = 3¹ × 17¹ × 587¹

Step-2: Prime Factorization of 29952

Prime factors of 29952 are 2, 3, 13. Prime factorization of 29952 in exponential form is:

29952 = 2⁸ × 3² × 13¹

Step-3: Factors of 29937

List of positive integer factors of 29937 that divides 29937 without a remainder.

1, 3, 17, 51, 587, 1761, 9979

Step-4: Factors of 29952

List of positive integer factors of 29952 that divides 29937 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 128, 144, 156, 192, 208, 234, 256, 288, 312, 384, 416, 468, 576, 624, 768, 832, 936, 1152, 1248, 1664, 1872, 2304, 2496, 3328, 3744, 4992, 7488, 9984, 14976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29937 and 29952. The biggest common factor number is the GCF number.
So the greatest common factor 29937 and 29952 is 3.

Also check out the Least Common Multiple of 29937 and 29952