## Question

The number of divisors a number 38808 can have, excluding 1 and the number itself is :

### Solution

70

38808 = 2^{3} . 3^{2} . 7^{2} . 11

No. of divisors = (3 + 1) . (2 +1) . (2 + 1) . (1 + 1)

= 4 × 3 × 3 × 2 = 72

But it includes 1 and the number itself

Hence required no. of divisors = 72 – 2 = 70.

#### SIMILAR QUESTIONS

10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys so that exactly 2 children do not get any toy, is equal to:

There are 20 persons among whom are two brothers. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers.

In how many ways can a party of 4 men and 4 women be seated at a circular table so that no two women are adjacent?

There are 5 gentlemen and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?

Find the number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated.

How many integral solutions are there to *x* + *y* +* z* + *t *= 29, when *x **≥* 1, y*≥ *2, *z* *≥ *3* *and *t* *≥ *0?

How many integral solutions are there to the system of equations

*x*_{1} + *x*_{2} + *x*_{3} + *x*_{4} + *x*_{5} = 20 and *x*_{1} + *x*_{2} + *x*_{3} = 5 when *x*_{k} ≥ 0?

There are *n* points in a plane of which no three are in a straight line except ‘*m*’ which are all in a straight line. Then the number of different quadrilaterals, that can be formed with the given points as vertices, is :

A father with 8 children takes 3 at a time go to the zoological Garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is :

In a class tournament when the participants were to play one game with another, two class players fell ill, having played 3 games each (*not played between them*). If the total number of games played is 84, the number of participants at the beginning was: