Question

11. Find the largest 3-digit number which leaves remainder 2 when divided by 14 or 35.

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Answer 1

Answer: 982 is the largest 3-digit number which when divided by 14 or 35 leaves remainder 2.

Given: We are given numbers 14 and 35 and remainder is given to be 2.

To Find: We have to find the largest 3-digit which when divided by 14 or 35 leaves remainder 2.

Step-by-Step Explanation: We will firstly find the largest 3-digit number which is divisible by both 35 and 14. To do so, we will multiply 35 with 14.

$35\times14=490$

Since 490 is the product of 35 and 14, it is divisible by both 35 and 14.

And any multiple of 490 will also be divisible by 35 and 14.

So, $490\times2=980$ is also divisible by 35 and 14.

980 is the largest 3-digit number which is multiple of 35 because after that 1015 will be the next multiple which is a 4-digit number.

Therefore, 980 is the largest number divisible by both 35 and 14.

And, hence 982 will be the largest 3-digit number that will leave remainder when divided by 35 or 14.

To know more about number theory, refer to the links below:

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