Decide which cube sizes pack a box with no gaps, and find the biggest number that divides two numbers.
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A size that fits all lengths exactly must be a common factor of all of them.
For cubes to fill a box with no gaps, the cube's edge must divide the length, the width and the height exactly.
So it must be a common factor of all three.
Which cube sizes fill the box with no gaps?
Problem. A box is 12 cm by 18 cm by 36 cm. Which of these cubes pack it with no gaps: 9 cm, 6 cm, 4 cm, 3 cm, 2 cm? (Textbook p. 64, Q6)
Pick the largest number that divides 306 and 36.
Which is the largest number that divides both 306 and 36? (Textbook p. 64, Q7)