Let's denote the number as 'n' and the divisor as 'd'.

From the problem, we know that:

1) n = kd + 5 (where k is some integer)
2) 8n = pd + 6 (where p is some integer)
3) 12n = qd + 9 (where q is some integer)

We can substitute the first equation into the second and third equations:

2) 8(kd + 5) = pd + 6
3) 12(kd + 5) = qd + 9

Solving these equations gives:

2) 8kd + 40 = pd + 6
3) 12kd + 60 = qd + 9

Rearranging these equations gives:

2) pd - 8kd = 34
3) qd - 12kd = 51

We can see that 34 and 51 have a common factor of 17. So, we can divide the second equation by 2 and the third equation by 3 to get:

2) (pd - 8kd)/2 = 17
3) (qd - 12kd)/3 = 17

This implies that the divisor 'd' must be a multiple of 17.

Therefore, the divisor is 17.

Question

Let's denote the number as 'n' and the divisor as 'd'.

From the problem, we know that:

1) n = kd + 5 (where k is some integer)
2) 8n = pd + 6 (where p is some integer)
3) 12n = qd + 9 (where q is some integer)

We can substitute the first equation into the second and third equations:

2) 8(kd + 5) = pd + 6
3) 12(kd + 5) = qd + 9

Solving these equations gives:

2) 8kd + 40 = pd + 6
3) 12kd + 60 = qd + 9

Rearranging these equations gives:

2) pd - 8kd = 34
3) qd - 12kd = 51

We can see that 34 and 51 have a common factor of 17. So, we can divide the second equation by 2 and the third equation by 3 to get:

2) (pd - 8kd)/2 = 17
3) (qd - 12kd)/3 = 17

This implies that the divisor 'd' must be a multiple of 17.

Therefore, the divisor is 17.

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