What is the Greatest Common Factor of 76128 and 76140?

Greatest common factor (GCF) of 76128 and 76140 is 12.

GCF(76128,76140) = 12

We will now calculate the prime factors of 76128 and 76140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76128 and 76140.

How to find the GCF of 76128 and 76140?

We will first find the prime factorization of 76128 and 76140. After we will calculate the factors of 76128 and 76140 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 76140

Prime factors of 76140 are 2, 3, 5, 47. Prime factorization of 76140 in exponential form is:

76140 = 2² × 3⁴ × 5¹ × 47¹

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 76140

List of positive integer factors of 76140 that divides 76128 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 47, 54, 60, 81, 90, 94, 108, 135, 141, 162, 180, 188, 235, 270, 282, 324, 405, 423, 470, 540, 564, 705, 810, 846, 940, 1269, 1410, 1620, 1692, 2115, 2538, 2820, 3807, 4230, 5076, 6345, 7614, 8460, 12690, 15228, 19035, 25380, 38070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76128 and 76140. The biggest common factor number is the GCF number.
So the greatest common factor 76128 and 76140 is 12.

Also check out the Least Common Multiple of 76128 and 76140