Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is

the least number of square pieces he can cut without wasting any of the board?

I would first check what is the greates common factor o 18 and 30. It is 6. So each side of the square would be 6 inches. The area you have to cover is 540 (18 x 30). You can thus cut out 15 squares of 6x6 inches.

Think of it conceptually. What is the first square you can try? You can fit multiple squares of 1x1 inches. But also squares of 2x2 inches. And since you have to find the least possible number, the square should be as big as possible. So keep going. 3x3 is equally possible. 4x4, 5x5 is not possible (18 is not divisible by them) but 6x6 is…

Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is

the least number of square pieces he can cut without wasting any of the board?

(A) 4

(B) 6

(C) 9

(D) 12

(E) 15

Basically, try to find Greatest Common Divisor of 18 and 30. In this case, 18= 2*3^2

30=5*2*3 , G.C.D. is 6, In total, we have 3*5=15 squares

You can also refer to this

Hi guys, as it is suggested in the 2-month plan, for week 1 day 1 - Do I need to do all of the Manhattan 5-lb chapter Divisibility and Primes Qs?

There are Qs like “Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is

the least number of square pieces he can cut without wasting any of the board?”

Can we skip such sort of Qs or especially this one? suggestions, please.

Aiming for 165+ in Q

If that is a 165+, then you shouldn’t skip this type of question

Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is

the least number of square pieces he can cut without wasting any of the board?

(A) 4

(B) 6

(C) 9

(D) 12

(E) 15

I got it right till GCF then I didn’t understand how the answer became 15?

GCF should be the length of the square piece right? So just calculate how many 6x6 pieces you can make from 18x30.

- You can either do by finding the total area of the rectangular piece and dividing it by the area of a single square piece.
- Or just see that the 18 inch side can be cut into 3 equal 6 inch sides, and the 30 inch sides can be cut into 5. So it’s 3 rows and 5 columns. So the number of squares is the product of them (rows and columns)

Thank you so much!