When you encounter questions that ask you for “the most” or “the least” possible options, they usually require you to find the Highest Common Factor (HCF) or Lowest Common Multiple (LCM) of 2 or more integers.
(a) to find the least, we must divide 630cm & 396cm by the largest possible factor.
To find HCF of 630, you must begin by dividing it with its largest prime number (in this case, 7) then dividing by lower prime numbers until it is fully divided.
630 = 2 x 3² x 5 x 7
396 = 2²x 3² x 11
Then, you multiply the lowest common factors
2 x 3² = 18 (H.C.F)
This is the largest possible length of a square. The second largest is found by dividing by 2.
3² = 9cm. (b)(i)
630cm ÷ 18cm = 35 squares
396cm ÷ 18cm = 22 squares
The retangular board can thus be cut into 35 squares length-wise, and 22 squares width-wise.
35 x 22 = 770 squares at least (a)
With a 9cm length, each square would be 9²= 81cm²
Take the board’s area divided by the squares’ area.
630cm x 396cm = 249480cm²
249480cm² ÷ 81cm² = 3080 squares (b)(ii)
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