SOLUTION: There are 72 boys and 90 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
Algebra ->
Divisibility and Prime Numbers
-> SOLUTION: There are 72 boys and 90 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
Log On
Question 939292: There are 72 boys and 90 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 by mathmate(429) (Show Source):
objective: to arrange in rows with equal number (n) of only boys or girls.
To find the maximum number (n) of boys or girls in each row, we need to find the GCF (Greatest Common Factor) of the numbers 72 and 90, such that n divides both numbers evenly without a remainder.
We will use two methods to find the GCF of two numbers.
Method 1
Factorize each number to powers of prime and locate the common factors.
So the GCF is
Method 2 (Euclid division)
step 1: divide the larger number by the small number, reject the quotient
step 2: if the remainder is 0, the smaller number is the GCF
if the remainder is greater than zero, replace the larger number by the remainder (which becomes the smaller number), repeat step 1.
We will use the folowing symbols
L=larger number
S=smaller number
R=remainder
L S R
90 72 18 with remainder 18
72 18 0 with remainder 0
Therefore 18 is the GCF
Answer: the students can be arranged in rows of 18, that is 4 rows of boys and 5 rows of girls.
