SOLUTION: Mrs. Jones has 18 boys and 27 girls in choirs. She wants them in equal rows. Only boys or girls will be in row(meaning no mixed rows). What is the greatest number of students that

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Mrs. Jones has 18 boys and 27 girls in choirs. She wants them in equal rows. Only boys or girls will be in row(meaning no mixed rows). What is the greatest number of students that       Log On


   

Question 1097998: Mrs. Jones has 18 boys and 27 girls in choirs. She wants them in equal rows. Only boys or girls will be in row(meaning no mixed rows). What is the greatest number of students that can stand in each row?
Found 3 solutions by Edwin McCravy, KMST, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
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The greatest common divisor, GCD, of 18 and 27, which is 9.

BBBBBBBBB    <--9 boys
BBBBBBBBB    <--9 boys
GGGGGGGGG    <--9 girls
GGGGGGGGG    <--9 girls
GGGGGGGGG    <--9 girls

Edwin

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
18=2%2A9 (or 18=2%2A3%5E2 if you prefer)
27=3%2A9 (or 27=3%5E3 if you prefer)
Both numbers are divisible by 9 ,
so Mrs. Jones could make rows of 9 students:
27%2F9=3 rows of girls, and
18%2F9=2 rows of boys.

NOTE:
If we have to mention vocabulary words,
18=2%2A3%5E2 and 27=3%5E3 are the prime factorizations of 18, and 27,
and 3%5E2=9 is the greatest common factor,
using all common prime factors (just 3),
with the least exponent found in the factorizations.

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
The tutor's @KMST explanation and solution is/are perfect.


So, the problem simply ask you to find the greatest common divisor of the numbers 18 and 27.

And this greatest common divisor (GCD) is 9.