The choir director is dividing the the sopranos and altos into groups. There will be sopranos and altos in each group. There are 10 sopranos and 15 altos. Each group will have the same number of altos. Each group will have the same number of sopranos. All sopranos and altos will be put in a group. No one is left out!

A. What is the greatest number of groups possible? Remember to label your answer.
B. How many sopranos will be in each group? Remember to label your answer.
C. How many altos will be in each group? Remember to label your answer.
D. Explain how you did it.

Question

The choir director is dividing the the sopranos and altos into groups.  There will be sopranos and altos in each group.  There are 10 sopranos and 15 altos.  Each group will have the same number of altos.  Each group will have the same number of sopranos.  All sopranos and altos will be put in a group.  No one is left out! 

A.  What is the greatest number of groups possible?  Remember to label your answer.
B.  How many sopranos will be in each group?  Remember to label your answer. 
C.  How many altos will be in each group?  Remember to label your answer.
D. Explain how you did it.

anonymous · Answer

@alakara_kibo 
@tester97

undeadknight26 · Answer

What number can go into both of them?

lastdaywork · Answer

"...A. What is the greatest number of groups possible?..."
If I say that the question is asking for the HCF ; can you explain why..

anonymous · Answer

@LastDayWork I don't know what the HCF is
@undeadknight26 No clue _-_

lastdaywork · Answer

Highest Common Factor
Also known as Greatest Common Divisor

anonymous · Answer

@LastDayWork I Have no clue.

anonymous · Answer

i just kind of want the answer but with a explanation :/

undeadknight26 · Answer

i think its C because there is an odd number of them making it impossible for them both be able to be divided into equal groups.

lastdaywork · Answer

@HB0102 
Under which topic you found the above question ??

anonymous · Answer

@LastDayWork Number Properties
@undeadknight26 it's a word problem. I have to write answers for A-D

undeadknight26 · Answer

oh now it makes sense...

lastdaywork · Answer

Lets solve (A) first -

As "...Each group will have the same number of altos.."
the number of groups should be a factor of 15
or
15 should be divisible by the number of groups

As "...Each group will have the same number of sopranos..."
the number of groups should be a factor of 10
or
10 should be divisible by the number of groups.

Now try to find the common factors of 10 and 15.

anonymous · Answer

Well the GCF is 5.

lastdaywork · Answer

Okay, so you call it GCF.
Can you see the line of reasoning here ??

anonymous · Answer

Yes...

lastdaywork · Answer

Can you answer B and C by yourself ??

anonymous · Answer

I don't know ??

anonymous · Answer

B is 2 and C is 3

anonymous · Answer

@alakara_kibo Can you explain how you got that answer?

anonymous · Answer

ok well u can have 5 groups and  There are 10 sopranos  well u divide that and get 2 for B and for C u got 15  altos so u divide this by 5 and get 3 so thats how i got my answer

anonymous · Answer

does this make sense to u?