When a number is divided by 13, the remainder is 10. When the same number is divided by 17, the remainder is 8. What is the number?  Options :329336348353

The problem can be solved using the Chinese Remainder Theorem.

Step 1: Write down the given conditions. We have two conditions: a) When a number is divided by 13, the remainder is 10. This can be written as x ≡ 10 (mod 13) b) When the same number is divided by 17, the remainder is 8. This can be written as x ≡ 8 (mod 17)

Step 2: Solve the equations. We need to find a number that satisfies both these conditions.

We can start by checking the options one by one.

Option 1: 329 329 divided by 13 gives a remainder of 10, and 329 divided by 17 gives a remainder of 8. So, 329 satisfies both conditions.

Therefore, the number is 329.