Question

10.a) Which numbers less than 100 have exactly 3 factors (including 1 and the number itself)?

b) Which two numbers less than 100 have exactly 5 factors?

c) Which number less than 100 has exactly 7 factors?

Answer 1

Explanation:

a)

any prime number has only 2 (1 and the number itself).

almost every even number has 1, 2, a factor of 2 and the number itself. so that did not work either.

following that line of thought, the only possible solutions are square numbers of prime numbers :

4, 9, 25, 49

they have only 1, its square root and the number itself as factors.

b)

in the same line of thinking it must be powers of 4 of prime numbers :

2⁴ = 16

with the factors 1, 2, 4, 8, 16

3⁴ = 81

with the factors 1, 3, 9, 27, 81

c)

and so, it must be a power of 6 of a prime number.

the only one possible is

2⁶ = 64

with the factors 1, 2, 4, 8, 16, 32, 64