Question

Find the highest positive integer by which dividing the numbers $396,436$ and $542$ remainders are $5,11$ and $15$ respectively

Answer 1

For $5$:

Dividing $396$ by $391$ gives remainder $5$. Clearly, $391$ is the largest positive integer to give remainder $5$.

Similarly, for $436$, the largest positive integer to give remainder $5$ is $436-5=431$

for $542$, the largest positive integer to give remainder $5$ is $542-5=537$

Continuing the above logic for remainder $11$,

For $396$, the largest positive integer to give remainder $11$ is $396-11=385$

For $436$, the largest positive integer to give remainder $11$ is $436-11=425$

For $542$, the largest positive integer to give remainder $11$ is $542-11=531$

Continuing the above logic for remainder $15$,

For $396$, the largest positive integer to give remainder $15$ is $396-15=381$

For $436$, the largest positive integer to give remainder $15$ is $436-15=421$

For $542$, the largest positive integer to give remainder $15$ is $542-15=527$