Latest Elitmus Aptitude Question SOLUTION: A natural number has exactly 10 divisors including 1 and itself. How many distinct prime factors can this natural number have? A. Either 1 or 2 B. Either 1 or 3 C. Either 2 or

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(#M40037916) ELITMUS Numerical Ability question Keep an EYE

A natural number has exactly 10 divisors including 1 and itself. How many distinct prime factors can this natural number have?

A. Either 1 or 2

B. Either 1 or 3

C. Either 2 or 3

D. Either 1,2 or 3

Asked In Elitmus Liti (9 years ago)

Unsolved Read Solution (5)

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MURALIDHARAN  (9 years ago)

Either 1 or 2
Reason : since given maximum factors is 10...this is obtained only by (9+1) or (4+1)*(1+1)

Since we know that for p1^a,p2^b.... are factors ,p1 and p2 are prime...then total factors are (a+1)*(a+2)....

by this way we can't split 10 not more than 2 ways...so answer is i or 2

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RAKESH KUMAR RANJAN  (9 years ago)

since we know that if a,b is prime factor of a number n.
and n=a^p*b^q
then number of divisor=(p+1)(q+1).
here given 10 divisor so possible factor of 10 is 1,10 or 2,5
so no of prime factors is either 1 or 2

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anonymous  (9 years ago)

let us take 120 = 1x2x3x4x5x6x8x10x12x120

here it have 3 prime factors

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sourav dev gupta  (9 years ago)

c is the correct answer

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LOKESH RANJAN  (9 years ago)

a,as a^p*b^q gives (p+1)*(q+1)

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