10. CBQ - Packing Grains

Question:

4 m.

A farmer has 72 \(kg\) of rice and 120 \(kg\) of wheat. Each bag must contain grain of only one kind. All bags must have the same whole-number weight, and the number of bags should be as small as possible.

Based on the above information answer the following questions:

(i) Write the prime factorisation of 72.

\(72 = 2 \times 2 \times 2 \times 3 \times 3\)
\(72 = 2 \times 2 \times 2 \times 3 \times 3\), \(29\)
\(72 = 2 \times 2 \times 2 \times 3 \times 3\), \(17\)
\(72 = 2 \times 2 \times 2 \times 3 \times 3\), \(11\)

(ii) Write the prime factorisation of 120.

\(120 = 2 \times 2 \times 2 \times 3 \times 5\) \(\times 23\)
\(120 = 2 \times 2 \times 2 \times 3 \times 5\) \(\times 13\)
\(120 = 2 \times 2 \times 2 \times 3 \times 5\) \(\times 19\)
\(120 = 2 \times 2 \times 2 \times 3 \times 5\)

(iii) What weight should each bag hold?

34
24
14
39

(iv) How many bags are needed in all?

7
10
8
9

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