Question

How many 4 digit number have exactly 5 factors?

Answer 1

Answer:

To get 5 factors the number should be of the form

Answer 2

How many 4-digit numbers have exactly 5 factors?

To find,

4-digit numbers having exactly 5 factors.

Solution,

Since factors always come in pairs (for example, (1, 6) and (2, 3) are factors of 6), numbers that have exactly 5 factors will have to be perfect squares - in a way that one of their factors are multiplied twice (for example, in the case of 16: (1,16), (2,8) and (4,4), the factors being 1,2,4,8 and 16).

The only numbers with exactly 5 factors are those that can be expressed as

${x}^{4}$

The first number which satisfies both conditions is 1296 (6*6*6*6)

Similarly, 7*7*7*7 = 2401

8*8*8*8 = 4096

9*9*9*9 = 6561

But 10*10*10*10 is 10000 which is a five-digit number.

So, the four-digit numbers having exactly 5 factors are 1296, 2401, 4096 and 6561.

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