Latest Elitmus Aptitude Question SOLUTION: a natural numbr has exactly 10 divisors including 1 and itself.how many distint prime factors this natural numbr will have? options: 1 or2 1 or3 1 or 2or 3 2 or 3

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(#M40153856) ELITMUS Numerical Ability question Keep an EYE

a natural numbr has exactly 10 divisors including 1 and itself.how many distint prime factors this natural numbr will have?
options: 1 or2
1 or3
1 or 2or 3
2 or 3

Asked In Elitmus Anjali Sadhukhan (8 years ago)

Unsolved Read Solution (11)

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RAJESH KUMAR  (8 years ago)

a) 1 or 2

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vivek  (8 years ago)

Here it is given that the number has exactly 10 divisor including 1 and itself.
So the number may be (any one prime factors)power 9 .....I.e (2)pow 9, (3)pow 9....etc.total 10 factor=(9+1)=10.
Also the number may be as (any one prime factors)pow 1*(any one prime factors)pow 4........I.e...(2)pow 1*(3)pow 4...etc= total 10 factor((1+1)*(4+1))=10.
Hence either 1 or 2 is correct answer.

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anand singh  (7 years ago)

Formula is : No of Divisor=a*b*c---- Where a-1, b-1, c-1 are no of occurence of that no in factor that no.
*Ex* - Find no of factor of 40
40=(2)^3*(5)^1
so no of factor of 40=(3+1)*(1+1)=8
Similarly,10=5*2 or(4+1)*(1+1)
=10*1 (9+1)*(0+1)
second case is not practical.
So, X^4*Y^1 is factor of that no.

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RAJESH KUMAR  (8 years ago)

Take no as 512 . then the divisors of this no. are
1,2,4,8,16,32,64,128,256,512;

so only one prime factors are there 2;

Suppose if the number is 48 the divisors are
1,2,3,4,6,8,12,16,24,48;
so the prime factors are 2,3;

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abhishek kumar deepak  (8 years ago)

1 or 2 or 3 also possible

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Anjali Sadhukhan  (8 years ago)

rajesh,,if you could explain how you solved it!!!!!!!!!!!!!

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ananga  (8 years ago)

@rajesh how can u directly take the nos??
is there any frmula??

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Neeraj Shukla  (8 years ago)

their is direct solution lel 36 as ans it cac factor as 2^2*3^2
now total sol is (2+1)*(2+1) =9 ie 36 have 9 factor including 1 and 36 itself.
now since i have no 10 it can only factorise as 2*5 ie(1+1)*(4+1).
so it have only two soln either 1 or 2. here 1 and 4 shows (x^1*Y^4)

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Anjali Sadhukhan  (8 years ago)

2 or 3.would be the ans.512,36,48

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Vikash kumar  (7 years ago)

1 or 2 is the correct answer

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Vikash kumar  (7 years ago)

correct answer is
explanation:
the factor of 10 =1,2,5,10
so ans is 1 or 2

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