Find the smallest integer that produces remainder of 2,4,6&1 when it is divided by 3,5,7&11 respectively?
1 Answer
Explanation:
Call the number
-
In order to give a remainder of
2 when divided by3 ,n must be one less than a multiple of3 . -
In order to give a remainder of
4 when divided by5 ,n must be one less than a multiple of5 . -
In order to give a remainder of
6 when divided by7 ,n must be one less than a multiple of7 .
So
3*5*7 = 105
So:
n = 105k-1" " for some integerk .
In order to give a remainder of
So we have:
11m+1 = 105k-1
That is:
105k = 11m + 2
Now:
105/11 = 9" " with remainder6
So what are the multiples of
1*6 = 6 = 0*11+6
2*6 = 12 = 1*11 + 1
3*6 = 18 = 1*11 + 7
4*6 = 24 = 2*11 + 2
So the smallest possible positive value of
So:
n = 105k-1 = 105*4-1 = 419