What is the Greatest Common Factor of 75678 and 75696?

Greatest common factor (GCF) of 75678 and 75696 is 6.

GCF(75678,75696) = 6

We will now calculate the prime factors of 75678 and 75696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75678 and 75696.

How to find the GCF of 75678 and 75696?

We will first find the prime factorization of 75678 and 75696. After we will calculate the factors of 75678 and 75696 and find the biggest common factor number .

Step-1: Prime Factorization of 75678

Prime factors of 75678 are 2, 3, 12613. Prime factorization of 75678 in exponential form is:

75678 = 2¹ × 3¹ × 12613¹

Step-2: Prime Factorization of 75696

Prime factors of 75696 are 2, 3, 19, 83. Prime factorization of 75696 in exponential form is:

75696 = 2⁴ × 3¹ × 19¹ × 83¹

Step-3: Factors of 75678

List of positive integer factors of 75678 that divides 75678 without a remainder.

1, 2, 3, 6, 12613, 25226, 37839

Step-4: Factors of 75696

List of positive integer factors of 75696 that divides 75678 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 83, 114, 152, 166, 228, 249, 304, 332, 456, 498, 664, 912, 996, 1328, 1577, 1992, 3154, 3984, 4731, 6308, 9462, 12616, 18924, 25232, 37848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75678 and 75696. The biggest common factor number is the GCF number.
So the greatest common factor 75678 and 75696 is 6.

Also check out the Least Common Multiple of 75678 and 75696