Question 83

The numbers of divisors of 1248 other than 1 and the numberitselfis:

Solution

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Factors of 1248 = 2 x 2 x 2 x 2 x 2 x 3 x 13

It can be written as 

1248 = $$2^{5}$$ x $$3^{1}$$ x $$13^{1}$$

Factors are written in the form: $$2^{p}$$ x $$3^{q}$$ x $$13^{r}$$

Total number of divisors = (p+1) x (q+1) x (r+1)

= (5+1) x (1+1) x (1+1)

= 6 x 2 x 2 = 24

1 and the number itself are excluded, then

24 - 2 = 22

So, the number of divisors will be 22.

Hence, option C is correct.

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