What whole number is nearest to 457 which is divisible by 11?

1. 462

2. 460

3. 451

4. 450

Given number = 457.

To find the nearest number divisible by 11 :

$\begin{array}{l} \phantom{x^21}{\quad 41} \ 11\overline{\smash{\big)}\quad 457} \ \phantom{x^ + )}\phantom{)}\underline{-44} \ \phantom{{x^2 } + 2a} 17 \ \phantom{{x} +1a}\underline{-11} \ \phantom{{x^2 } + 2xa } 6\ \end{array}$

The multiple of 11 just below 457 is 11 x 41 = 451.

The multiple of 11 just above 457 is 11 x 42 = 462.

Distance from 457 to 451: ∣457 − 451∣ = 6.

Distance from 457 to 462: ∣457 − 462∣ = 5.

The smaller distance is 5, which corresponds to the number 462.

Therefore, the whole number nearest to 457 that is divisible by 11 is 462.

Hence, option 1 is the correct option.