## School Musical Math Problem

At a school musical practice session, there are 32 tambourinists, 80 triangle beaters, 64 drummers, 112 maracas shakers, and 48 singers. The music teacher assigns the children to equal sized groups. Each group has the same number of singers, and players of each instrument.

What is the largest number of groups possible? (no student is left out)

*Answers to this challenge can be entered into the section below; submissions will automatically be revealed when time is up!*

RK| Founder | Profile April 12th, 2011 - 9:59 pmtest

suineg| PUZZLE MASTER | Profile April 12th, 2011 - 10:55 pmI think the answer is 16 groups.

My reasoning was to take each number to their prime factorization, so:

2 to the 4 is the least common multiple and its 16, so 16 groups:

Each of this 16 groups would have: 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers and 3 singers.

Cool!!

Vik| Profile April 13th, 2011 - 8:40 am173?

joe| Profile April 13th, 2011 - 9:13 amDont know if I did this one too quickly and I am wrong but

16 groups each with

2 tambourinists, 5 triangle beaters, 4 drummers, 7 maraca shakers and 3 singers

I looked for the HIGHEST common denominator..

engjs1960| Profile April 13th, 2011 - 9:25 am16 groups of 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers. Simple factoring problem.

Adam| Profile April 13th, 2011 - 9:33 am16 (the greatest common factor)

16 * 2 = 32

16 * 3 = 48

16 * 4 = 64

16 * 5 = 80

16 * 7 = 112

Mashplum| PUZZLE MASTER | Profile April 13th, 2011 - 10:37 am16.

The GCF of all the numbers is 16. Each group has 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers.

Bobo The Bear| PUZZLE MASTER | Profile April 13th, 2011 - 10:55 amThere can be 16 groups (Each group has 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers).

suropriya| Profile April 13th, 2011 - 12:22 pmThe largest number is 16

suropriya| Profile April 13th, 2011 - 12:25 pm16

Hex| PUZZLE MASTER | Profile April 13th, 2011 - 12:52 pm16 groups as 16 is the greatest common divisor to 32, 48, 64, 80, and 112

John Lewis Highsmith| Profile April 13th, 2011 - 8:39 pmThe maximum number of groups is 16 – giving 2 tambourine shakers, 5 triangle players, 4 drummers. 7 maracas shakers, and 3 singers per group.

Shawn| PUZZLE GRANDMASTER | Profile April 14th, 2011 - 9:06 amSounds like 16 groups with 21 musicians in each group.

cheddarmelt| Profile April 15th, 2011 - 9:00 pm16. It’s the greatest common factor.

Each group will have 2 tambourinists, 5 triangle beaters, 4 drummers, 7 maracas shakers, and 3 singers.

joshuasteve| Profile April 25th, 2011 - 2:56 am16

dilipsethi| Profile April 28th, 2011 - 6:50 am16

Links to music and content area websites! | Melissa Schartz| Guest April 7th, 2013 - 6:18 pm[...] http://pbskids.org/cyberchase/.....rn-player/ http://www.smart-kit.com/s7477.....h-problem/ [...]

keerthi| Profile August 20th, 2013 - 3:37 am16 groups