The dimensions of a window are 156 cm $\times$ 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
The side of the largest square must divide both dimensions exactly, so we need HCF(156, 216).
Prime factorisation:
$$156 = 2^2 \times 3 \times 13$$
$$216 = 2^3 \times 3^3$$
HCF(156, 216) = $2^2 \times 3 = 12$ cm
Side length of each square = 12 cm
Number of squares along length = $156 \div 12 = 13$
Number of squares along breadth = $216 \div 12 = 18$
Total number of squares = $13 \times 18 = 234$
Source: Chapter 1, Section 1.2 – The Fundamental Theorem of Arithmetic
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Explanation
- The key insight: "maximum size" of a complete square that fits both dimensions → HCF of the two dimensions.
- Always show prime factorisation clearly; examiners award 1 mark for it.
- Finding HCF gets 1 mark; computing the number of squares gets the final mark.
- Don't forget to multiply both directions to get total squares — a common omission.