What is the Greatest Common Factor of 29952 and 29970?

Greatest common factor (GCF) of 29952 and 29970 is 18.

GCF(29952,29970) = 18

We will now calculate the prime factors of 29952 and 29970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29952 and 29970.

How to find the GCF of 29952 and 29970?

We will first find the prime factorization of 29952 and 29970. After we will calculate the factors of 29952 and 29970 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 29970

Prime factors of 29970 are 2, 3, 5, 37. Prime factorization of 29970 in exponential form is:

29970 = 2¹ × 3⁴ × 5¹ × 37¹

Step-3: Factors of 29952

List of positive integer factors of 29952 that divides 29952 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

Step-4: Factors of 29970

List of positive integer factors of 29970 that divides 29952 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 81, 90, 111, 135, 162, 185, 222, 270, 333, 370, 405, 555, 666, 810, 999, 1110, 1665, 1998, 2997, 3330, 4995, 5994, 9990, 14985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29952 and 29970. The biggest common factor number is the GCF number.
So the greatest common factor 29952 and 29970 is 18.

Also check out the Least Common Multiple of 29952 and 29970