On dividing 1653 by a certain number, we get 45 as quotient and 33 as remainder. Find the divisor.

Given:

Dividend = 1653

Quotient = 45

Remainder = 33

Using the formula,

Dividend = (Divisor × Quotient) + Remainder

Substituting the values, we get :

⇒ 1653 = (Divisor × 45) + 33

⇒ Divisor × 45 = 1653 - 33

⇒ Divisor × 45 = 1620

⇒ Divisor = $\dfrac{1620}{45}$

$\begin{array}{l} \phantom{x^2 }{\quad 36} \ 45\overline{\smash{\big)}1620} \ \phantom{x}\phantom{)}\underline{-135} \ \phantom{{x^2 }+} 270 \ \phantom{{x} +}\underline{-270} \ \phantom{{x^2 a}+} 0\ \end{array}$

⇒ Divisor = 36

Hence, the divisor = 36.