Latest Elitmus Aptitude Question SOLUTION: a natural no has exactly 10 divisors including 1 and itself.how many distinct prime factors can this no have?

• Placement Papers
• /
• Elitmus

Elitmus Question Papers:

(#M40018615) ELITMUS question Keep an EYE

a natural no has exactly 10 divisors including 1 and itself.how many distinct prime factors can this no have?

Asked In Elitmus priya jaswani (11 years ago)

Unsolved Read Solution (4)

Is this Puzzle helpful?   (0)   (1) Submit Your Solution

Read Solution (4) :

KARTHIGA DEVI.J  (11 years ago)

The number can have two distinct prime numbers.
10 can be written as 1*10 and 5*2
By rule (a+1)(b+1) should give 10
So (4+1)(1+1)=10.
thus two distinct prime numbers.

Is this solution Helpfull? Yes (10) | No (12)  

ravi kumar@gpcet  (11 years ago)

actually options for these question are:
a)only 1 b)either 1 or 2 c)2 prime factors d) either 1 or 2 or 3 prime factors
write sequence such that you invove minimum number of prime numbers in the sequence:
involve only 1 prime number i.e., 2 and write sequence upto 10 number in the following procedure:
->1 2 4 8(2*4) 16(8*2) 32(16*2) 64(16*4) 128 256 512 1024:
number is 1024 having 10factors including 1 and itself including 1 prime factor i.e., 2
now involve 2 prime numbers 2 and 3 by u r self in the sequence
->1 2 3 6 12 18 24 36 54 72:number is 72 and no of primes is 2(i.e., 2 and 3)
similarly another sequence in the same way
-> 1 2 3 5 10 15 20 30 40 50 :number is 50 and no of prime factors is 3 i.e., 1,2,3
so from all the above conditions the answer is d) either 1 or 2 or 3

Is this solution Helpfull? Yes (5) | No (11)  

sushmita nigam  (11 years ago)

10=10*1
in this case a no can have one single prime no as a divisor.
eg 512=2^9
this will have exactly(9+1)=10 divisors and only 2 as a prime no divisor.
10=5*2
in this case the number may have 2 prime no as divisors.
so the answer is- 1 or 2

Is this solution Helpfull? Yes (5) | No (1)  

SAMBIT KUMAR GHOSH  (11 years ago)

what is the xaact soln......@ravi,karthiga???

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.