What is the Greatest Common Factor of 15678 and 15684?

Greatest common factor (GCF) of 15678 and 15684 is 6.

GCF(15678,15684) = 6

We will now calculate the prime factors of 15678 and 15684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15678 and 15684.

How to find the GCF of 15678 and 15684?

We will first find the prime factorization of 15678 and 15684. After we will calculate the factors of 15678 and 15684 and find the biggest common factor number .

Step-1: Prime Factorization of 15678

Prime factors of 15678 are 2, 3, 13, 67. Prime factorization of 15678 in exponential form is:

15678 = 2¹ × 3² × 13¹ × 67¹

Step-2: Prime Factorization of 15684

Prime factors of 15684 are 2, 3, 1307. Prime factorization of 15684 in exponential form is:

15684 = 2² × 3¹ × 1307¹

Step-3: Factors of 15678

List of positive integer factors of 15678 that divides 15678 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 67, 78, 117, 134, 201, 234, 402, 603, 871, 1206, 1742, 2613, 5226, 7839

Step-4: Factors of 15684

List of positive integer factors of 15684 that divides 15678 without a remainder.

1, 2, 3, 4, 6, 12, 1307, 2614, 3921, 5228, 7842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15678 and 15684. The biggest common factor number is the GCF number.
So the greatest common factor 15678 and 15684 is 6.

Also check out the Least Common Multiple of 15678 and 15684