Câu hỏi của Chu Thanh Tùng

Question

A 3 - digit number when divided by 57, the remainder is 27, when divided by 217 the remainder is 60. Find the number.

Nguyễn Anh Kim Hân · Accepted Answer

Call a is the 3-digit number which divied by 57, the remainder is 27, divided by 217, the remainder is 60.

$\Rightarrow$a-27$⋮$57

$\Rightarrow$a-60$⋮$217

Because 684 is a multiple of 57 so:

$\Rightarrow$a-27-684$⋮$57$\Rightarrow$a-771$⋮$57

Because 651 is a multiple of 217 so:

$\Rightarrow$a-60-651$⋮$217$\Rightarrow$a-771$⋮$217

$\Rightarrow$a-771 $\in$CM(217;57)

$\Rightarrow$a-771$\in${0;12369;...}

$\Rightarrow$a$\in${771;13140;...}

Because a is a 3-digit number so a = 771.

The number is 771.Câu trả lời: Call a is the 3-digit number which divied by 57, the remainder is 27, divided by 217, the remainder is 60.