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# The nearest integer to 58701 which is divisible by 567 is A. 58968B. 58434C. 58401D. None

Last updated date: 02nd Aug 2024
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Hint: The given integer is 58701 and we need to divide the number by 567 and we get the remainder to be 300 and when we subtract that from 567 we get 267, hence adding 267 to the given integer we get the required answer.

Complete step by step solution:
We are given an integer 58701
We need to find a number nearer to 58701 which is divisible by 567
So now first let's divide the given integer by 567
$\Rightarrow 567\mathop{\left){\vphantom{1\begin{gathered} 58701 \\ \underline {58401} \\ 00300 \\ \end{gathered} }}\right. \!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered} 58701 \\ \underline {58401} \\ 00300 \\ \end{gathered} }}} \limits^{\displaystyle \,\,\, {103}}$
Hence we get the remainder to 300
Since $567 - 300 = 267$
Whenever we add another 267 with 300 we get 567 which is divisible by 567
So adding 267 to 58701 we get
$\Rightarrow 58701 + 267 = 58968$
Which is divisible by 567
Hence the number nearer to 58701 which is divisible by 567 is 58968

Therefore the correct answer is option A.

Note :
Many students tend to select 58401 as the answer as it is divisible by 567.
But we can see the difference between 58701 and 58401 is 300 and the difference between 58701 and 58968 is 267.
Hence 58968 is nearer to 58701 than 58401.