Question

what is the smallest number which when divided by 10 gives remainder 9 when divided by 9 gives remainder 8 when divided by 8 gives remainder 7 and so on down to remainder 1 when divided by 2 ​

Answer 1

Step-by-step explanation:

A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7. What is the number?

Required number = LCM(10,9,8) -1

= 359

Note : Each of dividend || divisor pair leaves -1 as remainder.

:-)

Let N be our number of interest.

N=10k+9, or (N+1) is divisible by 10

N=9m+8, or (N+1) is divisible by 9

N=8n+7, or (N+1) is divisible by 8, where k,m,n are integer numbers

Therefore, N+1 is a multiple of 8,9,10. LCM (least common multiple) of 8,9,10 is 360, and N+1 is a multiple of 360.

So N+1=360,720,1080…

Any number having the form 360 n -1 does the trick.

Answer 2

Answer:

the smallest number which when divided by 10 gives remainder 9 when divided by 9 gives remainder 8 when divided by 8 gives remainder 7 and so on down to remainder 1 when divided by 2