Prime factorization (6th grade common core math)

Question

A rectangle board game measures 126 cm by 90 cm. 

The game board is divided into small squares of equal size.

Find the longest possible length of the side of one of the small squares.

Answer 1

126=6*21=2*3*3*7

90=9*10=3*3*2*5=2*3*3*5

GCF=2*3*3=18 cm for the side of the square

Answer 2

you are looking for the GCF of 126 and 90

 

90 = 2 x 3 x 3 x 5

 

126 = 2 x 3 x 3 x 7

 

GCF = 2 x 3 x 3 = 18

 

So the squares will be 18 cm on a side.

 

you can get 5 across and 7 down for a total of 35 equal squares

 

the total area of all the squares is 35 x 18 x 18 = 11340 sq cm

 

and the area of the original rectangle is 126 x 90 = 11340 sq. cm

 

As expected, the areas are equal