Question

Ananya has 38 sharpners, 152 pencils and 114 erasers. How many maximum number of each one pencil box contains if she wants to pack same number of each in a number of pencil boxes.

• A. 2 sharpner,
  3 pencils,
  3 erasers
• B. 4 sharpner,
  3 pencils,
  1 erasers
• C. 1 sharpner,
  4 pencils,
  3 erasers
• D. 1 sharpner,
  3 pencils,
  4 erasers

Answer 1

The correct option is C 1 sharpner,

4 pencils,
3 erasers
To find the highest number of each item one pencil box can contain, we need to find the HCF of the 3 given numbers and pick the corresponding left over factor at the end.

$\begin{array}{cc}2& 38,152,114\\ 19& 19,76,57\\ & 1,4,3\end{array}$

Since there are no common factors for 1, 4 and 3 we cannot factorise it further.

The last row indicates the number of each corresponding item in one box.

Hence there will be 1 sharpner, 4 pencils and 2 erasers in each pencil box.