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A hall floor measures 16 m by 20 m. It is covered exactly by equal square tiles, each made as big as it possibly can be. How many tiles are needed?

Class 6Playing with NumbersPlaying with Numbers
  • A4
  • B5
  • C20
  • D320

Step-by-Step Solution

The biggest usable tile has side HCF(16, 20) = 4 m. That gives 16 ÷ 4 = 4 tiles along one wall and 20 ÷ 4 = 5 tiles along the other, so tiles in all. The traps: 4 is the tile's SIDE rather than the count, and 320 is the floor area in square metres.
Answer: C) 20

Key idea: Factors come in pairs

To find every factor of a number, walk up from 1 and check each whole number — if it divides the number with no remainder, it is a factor. Factors come in **pairs**: if 4 is a factor of 12, so is 12 ÷ 4 = 3. So you only need to check up to the square root of the number to find them all. Factors of 12: — six factors total: 1, 2, 3, 4, 6, 12. Every number has 1 and itself as factors.

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