What is the Greatest Common Factor of 76128 and 76146?

Greatest common factor (GCF) of 76128 and 76146 is 6.

GCF(76128,76146) = 6

We will now calculate the prime factors of 76128 and 76146, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76128 and 76146.

How to find the GCF of 76128 and 76146?

We will first find the prime factorization of 76128 and 76146. After we will calculate the factors of 76128 and 76146 and find the biggest common factor number .

Step-1: Prime Factorization of 76128

Prime factors of 76128 are 2, 3, 13, 61. Prime factorization of 76128 in exponential form is:

76128 = 2⁵ × 3¹ × 13¹ × 61¹

Step-2: Prime Factorization of 76146

Prime factors of 76146 are 2, 3, 7, 37. Prime factorization of 76146 in exponential form is:

76146 = 2¹ × 3¹ × 7³ × 37¹

Step-3: Factors of 76128

List of positive integer factors of 76128 that divides 76128 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 61, 78, 96, 104, 122, 156, 183, 208, 244, 312, 366, 416, 488, 624, 732, 793, 976, 1248, 1464, 1586, 1952, 2379, 2928, 3172, 4758, 5856, 6344, 9516, 12688, 19032, 25376, 38064

Step-4: Factors of 76146

List of positive integer factors of 76146 that divides 76128 without a remainder.

1, 2, 3, 6, 7, 14, 21, 37, 42, 49, 74, 98, 111, 147, 222, 259, 294, 343, 518, 686, 777, 1029, 1554, 1813, 2058, 3626, 5439, 10878, 12691, 25382, 38073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76128 and 76146. The biggest common factor number is the GCF number.
So the greatest common factor 76128 and 76146 is 6.

Also check out the Least Common Multiple of 76128 and 76146