What is the Greatest Common Factor of 15678 and 15696?

Greatest common factor (GCF) of 15678 and 15696 is 18.

GCF(15678,15696) = 18

We will now calculate the prime factors of 15678 and 15696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15678 and 15696.

How to find the GCF of 15678 and 15696?

We will first find the prime factorization of 15678 and 15696. After we will calculate the factors of 15678 and 15696 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 15696

Prime factors of 15696 are 2, 3, 109. Prime factorization of 15696 in exponential form is:

15696 = 2⁴ × 3² × 109¹

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 15696

List of positive integer factors of 15696 that divides 15678 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 109, 144, 218, 327, 436, 654, 872, 981, 1308, 1744, 1962, 2616, 3924, 5232, 7848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15678 and 15696. The biggest common factor number is the GCF number.
So the greatest common factor 15678 and 15696 is 18.

Also check out the Least Common Multiple of 15678 and 15696