Question

There are 727272 boys and 909090 girls on the math team. for the next math competition, mr. johnson would like to arrange all of the students in equal rows with only girls or only boys in each row. what is the greatest number of students that can be in each row?

Answer 1

Given that there are 72 boys and 90 girls on math team.

Mr. Johnson like to arrange all of the students in equal rows with only girls or boys in each row.

Let n be the maximum number of boys are girls in each row. Then we have to such number which divides both 72 and 90. So basically here we are going to find greatest common factor of 72 and 90

First completely factorize 72 and 90

72 = 2 * 36

= 2 *2 * 18

=2 * 2 * 2 * 9

72 =2 * 2 * 2 * 3 * 3

Similarly 90 = 2 * 45

= 2 * 3 * 15

90 = 2 * 3 * 3* 5

Now we have 72 = 2 * 2 * 2 * 3 * 3 and 90 = 2 * 3 * 3 * 5

Now we will find the common factor in both which are 2 ,3 ,3

So Greatest common factor = 2 * 3 * 3= 18

It means in each row there can be maximum 18 students.

The greatest number of students that can be in each row is 18