Question

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

Solution

Correct option is

70

38808 = 23 . 32 . 72 . 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

Q1

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:

Q2

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.

Q3

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?

Q4

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?

Q5

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.

Q6

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

Q7

How many integral solutions are there to the system of equations

x1 + x2 + x3 + x4 + x5 = 20 and x1 + x2 + x3 = 5 when xk ≥ 0?

Q8

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 :

Q9

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 :

Q10

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: