Question

Kant's sister has 150 red marbles and 360 pink marbles and she wants the same number of marbles on each row, what is the least number of rows she can make ?

Answer 1

We know that Kant's sister has 150 red marbles and 360 pink marbles.

She separates the marbles in rows, such that each row must have the same number of marbles.

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)

Here we can see that the factors: 2, 3, and 5 appear (at least) one time in each number, this means that the 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.

and we will have:

150/30 = 5 rows of red marbles

360/30 = 12 rows of pink marbles.

A total of 5 + 12 = 17 rows.