Question

Jazmin is completing an art project. She has two pieces of construction paper. The first piece is 444444 cm wide and the second piece is 333333 cm wide.

Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible.
How wide should Jazmin cut each strip?

Answer 1

To find the width of each strip that Jazmin should cut, we need to find the greatest common divisor (GCD) of 444444 and 333333. The GCD is the largest number that divides evenly into both numbers without leaving a remainder.

We can find the GCD using the Euclidean algorithm, which involves repeatedly replacing the larger number with the remainder of the larger number divided by the smaller number, until the smaller number is equal to 0. The GCD is then the last non-zero number in this sequence.

In this case, we start by dividing 444444 by 333333:

444444 / 333333 = 1 with a remainder of 111111
We then divide the smaller number (333333) by the remainder (111111):

333333 / 111111 = 3 with a remainder of 0
Since the remainder is 0, the GCD is equal to the smaller number (333333). Therefore, Jazmin should cut each strip to have a width of 333333 cm.