What is the Greatest Common Factor of 75678 and 75684?

Greatest common factor (GCF) of 75678 and 75684 is 6.

GCF(75678,75684) = 6

We will now calculate the prime factors of 75678 and 75684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75678 and 75684.

How to find the GCF of 75678 and 75684?

We will first find the prime factorization of 75678 and 75684. After we will calculate the factors of 75678 and 75684 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 75684

Prime factors of 75684 are 2, 3, 7, 17, 53. Prime factorization of 75684 in exponential form is:

75684 = 2² × 3¹ × 7¹ × 17¹ × 53¹

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 75684

List of positive integer factors of 75684 that divides 75678 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 53, 68, 84, 102, 106, 119, 159, 204, 212, 238, 318, 357, 371, 476, 636, 714, 742, 901, 1113, 1428, 1484, 1802, 2226, 2703, 3604, 4452, 5406, 6307, 10812, 12614, 18921, 25228, 37842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75678 and 75684. The biggest common factor number is the GCF number.
So the greatest common factor 75678 and 75684 is 6.

Also check out the Least Common Multiple of 75678 and 75684