Hello Rae!Â

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 3Â² x 5 x 7

396 = 2Â²x 3Â² x 11

Then, you multiply the lowest common factors

2 x 3Â² = 18 (H.C.F)

This is the largest possible length of a square. The second largest is found by dividing by 2.

**3Â² = 9cm. (b)(i)**

630cm Ã· 18cm = 35 squares

396cm Ã· 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**Â at least **(a)**

With a 9cm length, each square would be 9Â²= 81cmÂ²

Take the board’s area divided by the squares’ area.

630cm x 396cm = 249480cmÂ²

249480cmÂ² Ã· 81cmÂ² = **3080 squares (b)(ii)**

Hope this helps you understand the question better! If you need help, just let us know ðŸ™‚