Question

Kristin’s three-year old sister is trying to arrange pink and red Starbursts in rows. She has 360 pink Starbursts and 150 red Starbursts. She wants to arrange them in rows so that there are either only pink or only red Starbursts in each row, and so that each row has the same number of Starburts. What is the least number of rows she can make?

Answer 1

A total of 5 + 12 = 17 rows.

The least number of rows she can make is when she puts N marbles in each row, such that N is the greatest common factor between 150 and 360.

To find the greatest common factor between 150 and 360 we can write them as the product of prime numbers.

150 = 15*10 = (3*5)*(2*5)

360 = 36*10 = (6*6)*(2*5) = (2*3*2*3)*(2*5)

greatest common factor between 150 and 360 is the product of these 3 factors:

GCF = 2*3*5 = 30

this means that we need to make rows with 30 marbles each.

150/30 = 5 rows of red marbles

360/30 = 12 rows of pink marbles.

A total of 5 + 12 = 17 rows.

Answer 2

To find the least number of rows she can make will be found by finding the biggest way to divide these into equal groups (greatest common factor).

You can use prime factorizations of each number to find the gcf.

150 - 2 x 3 x 5 x 5
360 - 2 x 2 x 2 x 3 x 3 x 5

The common prime numbers are 2 x 3 x 5

You can make 12 (360/30) rows of pink and 5 (150/30) rows of red.