Question

775,710 teenagers voted for their favorite singer on a TV show. Each singer received the exact same number of votes. How many singers could there have been?a) 5b) 2c) 6d) 9

Answer 1

There could have been 2,5,6, and 9 singers

1) Regarding 775,710 as an even number then for sure there could have been 2 singers on this TV Show

`775710\colon2=387,855`

2) On the other hand, 775710 is also divisible by 5, for its last number is 0. So there could also have been 5 singers.

`775710\colon5=155,142`

3) This number of teenagers can also be divided by 6 (for it is divisible by 2 and by 3) and by 9 as well ( the sum of the digits of 775710, 7+7+5+7+1+0=27 is also divisible by 9).

Hence, there could have been 2,5,6, and 9 singers since 775,710 can be divided exactly by 2,5,6, and 9.