Discussion

Explanation:

Let N = ‘ab’, where a and b are digits
N = 10a + b

Now, since a is a factor of ‘ab’, a should divide (10a + b) completely.
i.e., $R\left[\frac{10a+b}{a}\right]$ = 0

⇒ $R\left[\frac{10a}{a}\right]$ + $R\left[\frac{b}{a}\right]$ = 0

⇒ $R\left[\frac{b}{a}\right]$ = 0

∴ ‘b’ should be divisible by a.

If a = 1, b can be 0, 1, 2, 3, …, 9 ⇒ 10 possible values
If a = 2, b can be 0, 2, 4, 6, 8 ⇒ 5 possible values
If a = 3, b can be 0, 3, 6, 9 ⇒ 4 possible values
If a = 4, b can be 0, 4, 8 ⇒ 3 possible values

Number of possible values of ‘N’ = 10 + 5 + 4 + 3 = 22.

Hence, 22.

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