Question

[Khách]

What is the largest number, which when divided to 11 has a quoitient is equal to the số dư

Answer 1

[Nguyễn Hoàng Minh]

Call the dividend is \(a\), the remainder is \(b\left(b\le10;b\in N\right)\)

So the quotient is \(b\)

Have: \(a=11\times b+b=12\times b\)

So \(a_{max}\Leftrightarrow12\times b_{max}\Leftrightarrow b_{max}\Leftrightarrow b=10\)

\(\Leftrightarrow a=12\times10=120\)

So the largest number is 120