Important Number Questions
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Some typical number questions are given in this posts.The variants of the same questions are frequently coming in CAT and various other competitive exams like XAT,GMAT,MAT,IIFT,Symbiosis....So have a look at these questions...


1*Find the number of factors 24 has?

Explanation:-
24 can be written as 2^3*3.
We know that if N=a^m*b^n. Then the number of factors of N is (n+1)*(m+1)
Here we have, number of factors= (3+1) (1+1) = 8.

2*Find the least number with no. of factors as 24.

Explanation:-
A number can have 24 factors,
If its in the form, N=a^23,
or a*b^11
or a^2*b^7
or a^3*b^5
or a*b*c^5
or a*b*c*d^2 .

Here if we want to find the smallest number we need to fit in the smallest prime numbers as far as possible.
So better if you put the last choice, a*b*c*d^2, also put d=2,c=3,b=5,a=7
So the number becomes 2^2*3*5*7 ie
4*3*5*7= 420.
So this is the smallest number with 24 factors.
If we put any other forms of the number, the resulting number will be higher than 420.

*A number has unequal prime factors and the total number of factors is 4.
The sum of the factors without 1 and the number itself is 30. Find the smallest number with this characteristics.


Explanation:-
The number with 4 factors can be with the form a^3 or a*b.
Since its given that number has unequal prime factors, it can take the form of a*b.
Then the factors are 1, a, b, ab where ab is the number itself.
The condition given is a+b=30, where a and b are prime numbers.
a,b can be 7 & 23
11 & 19
13 & 17.
Then the smallest number is 7*23 = 161.

*How many numbers are there <1000, which has exactly 3 factors.

Only squares of prime numbers have exactly 3 factors.
So we need to find the number of prime number squares<1000.
The highest prime number square less than 1000 is 31^2.
So all prime number squares up to 31 can be regarded as the answer.
They are squares of 2,3,5,7,11,13,17,19,23,29,31.So there are total 11 numbers.
So answer is 11.

Feel free to post new questions in these topics..

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Comments (1)

On November 20, 2013 at 11:56 PM , Unknown said...

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