What is the Greatest Common Factor of 29952 and 29972?

Greatest common factor (GCF) of 29952 and 29972 is 4.

GCF(29952,29972) = 4

We will now calculate the prime factors of 29952 and 29972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29952 and 29972.

How to find the GCF of 29952 and 29972?

We will first find the prime factorization of 29952 and 29972. After we will calculate the factors of 29952 and 29972 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 29972

Prime factors of 29972 are 2, 59, 127. Prime factorization of 29972 in exponential form is:

29972 = 2² × 59¹ × 127¹

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 29972

List of positive integer factors of 29972 that divides 29952 without a remainder.

1, 2, 4, 59, 118, 127, 236, 254, 508, 7493, 14986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29952 and 29972. The biggest common factor number is the GCF number.
So the greatest common factor 29952 and 29972 is 4.

Also check out the Least Common Multiple of 29952 and 29972