Janet has 28 green beads, 84 red beads and 56 orange beads. She wants to pack them such that each bag contains the same number of beads of each color. What is the greatest number of bags she can pack?

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Solution

The correct option is A 28
To find the highest number of bags she can pack, we need to find the HCF of the given three numbers.

$\begin{matrix} 2 & 28, 84, 56 2 & 14, 42, 28 7 & 7, 21, 14 1, 3, 2 \end{matrix}$

Since there are no common factors for 1, 3 and 2 we cannot factorise it further.
Hence the HCF of 28, 84 and 56 is
$2 \times 2 \times 7 = 28$

Therefore, she can pack 28 bags, each containing 1 green bead, 3 red beads and 2 orange beads.

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