A number when divided by 259 leaves a remainder 139. What will be the remainder when the same number is divided by 37?

1. Break Down the Problem

We have a number $N$ that leaves a remainder of 139 when divided by 259. We need to find the remainder when $N$ is divided by 37.

2. Relevant Concepts

According to the division algorithm, we can express the number as: $N = 259k + 139$ for some integer $k$. To find the remainder of $N$ when divided by 37, we will calculate: $N \mod 37$

3. Analysis and Detail

Firstly, we need to compute $259 \mod 37$: $259 \div 37 \approx 7 \quad \text{(integer part)}$ Calculating $7 \times 37 = 259$: So, $259 \mod 37 = 0$

Next, we find $139 \mod 37$: $139 \div 37 \approx 3 \quad \text{(integer part)}$ Calculating $3 \times 37 = 111$: So, calculating the remainder: $139 - 111 = 28$ Thus, $139 \mod 37 = 28$

Now substituting back into our expression for $N$: $N \mod 37 = (259k + 139) \mod 37 = (0k + 28) \mod 37 = 28$

4. Verify and Summarize

We confirmed that:

• $259 \mod 37 = 0$
• $139 \mod 37 = 28$

This leads us to conclude that when $N$ is divided by 37, the remainder is:

Final Answer

$\boxed{28}$