a bus is full of passengers. if you count them by either twos, threes, or fives, there is one left. if you count them by seven there will be none left. find the least number of passengers in the bus?

91

Explanation:

You know that the number must end in 6 or 1 to get a left over of 1 when divided by 5. Six won't work because  2  divides evenly into a number ending into 6.

So the number ends in 1.

21 doesn't work because 3 divides into 21 evenly.

31 doesn't work because 7 does not divide into it.

41 doesn't work. 41 is prime. 7 won't divide into it.

51 is divisible by 3

61 seven does not evenly divide into 61.

71 seven leaves a remainder of  1

81 7 leaves a remainder.

91 Answer