what is this number?

Question

When you divide it by 2 you get a remainder of 1.

When you divide it by 3 you get a remainder of 1.

When you divide it by 4 you get a remainder of 1.

When you divide it by 6 you get a remainder of 1.

When you divide it by 7 you get no remainder

Answer 1

find the least common multiple of 2, 3, 4, 6, and 7

2=2

3=3

4=2*2

6=2*3

7=7

LCM=2*3*2*7

LCM=84

you must have a multiple of 7 to have no remainder when dividing by 7

it must be an odd number multiple of 7 because if it were an even number it would be divisible by 2

start with 84

add 7 to get 91 but 91/4=22 R3 so 91 is not the answer

add 14 to get 105 because you need an odd number but 105/6=17 R3 so 105 is not the answer

add 14 to get 119 but 119/3=39 R2 so 119 is not the answer

add 14 to get 133

133/2=66 R1

133/3=44 R1

133/4=33 R1

133/6=22 R1

133/7=19 R0

133 is the number

Answer 2

The last given fact means that the number is a multiple of 7.

A mere 7 divided by 4 goes not give a REMAINDER of 1, so try 14. Well that fails, because div by 2 doesn't give rem 1,

so try 21. Reject that because div by 3 doesn't get rem 1. 

 

What if we try 4•3•7+1?  This appears to be divisible by 2, by 3, by 4, by 6, all, with remainder 1.  Check it out.

Do you see why?