What is the Greatest Common Factor of 15678 and 15691?

Greatest common factor (GCF) of 15678 and 15691 is 13.

GCF(15678,15691) = 13

We will now calculate the prime factors of 15678 and 15691, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15678 and 15691.

How to find the GCF of 15678 and 15691?

We will first find the prime factorization of 15678 and 15691. After we will calculate the factors of 15678 and 15691 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 15691

Prime factors of 15691 are 13, 17, 71. Prime factorization of 15691 in exponential form is:

15691 = 13¹ × 17¹ × 71¹

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 15691

List of positive integer factors of 15691 that divides 15678 without a remainder.

1, 13, 17, 71, 221, 923, 1207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15678 and 15691. The biggest common factor number is the GCF number.
So the greatest common factor 15678 and 15691 is 13.

Also check out the Least Common Multiple of 15678 and 15691