Question

The number of divisors of an odd number is 34. If such a number is multiplied by 16. how man
divisors will it have?
0 544
0 170
0 165
0 136
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Answer 1

Answer:

67

Step-by-step explanation:

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Answer 2

b) 170 is the answer.

Given,

An odd number with 34 divisors.

To find,

The number of divisors when multiplied by 16.

Solution,

For a number N, the number of divisors is (a + 1)(b + 1)(c + 1)(d + 1)

where a,b,c,d are the number of times, a particular prime number appears.

The given number is odd. So, when multiplied by 16, a new prime number 2 will be present.

The number of divisors then becomes,

( number of times prime factor 2 appears + 1)(a + 1)(b + 1)(c + 1)(d + 1)

(4 + 1)(a + 1)(b + 1)(c + 1)(d + 1)

Here, (a + 1)(b + 1)(c + 1)(d + 1) represents the number of divisors the number originally had.

(4 + 1)(a + 1)(b + 1)(c + 1)(d + 1) = 5*34 = 170

Therefore, the new number will have 170 divisors.