Question

Find the remainder when 123456789...100 divided by 16

Answer 1

Answer:

Remainder is 9 when first 100 natural number is divided by 16.

Answer 2

Answer: Remainder will be 10

Given ,

We need to first be familiar with the 16 divisibility rule. Any integer will be a multiple of 16 if its final four digits can be divided by 16.

To Find ,

Finding the final four digits of the given number is the primary job. Find them together.

Solution ,

1–9 => 9 digits

10 - 100=90 digits

Every number following nine has two digits, hence there are (90/2)=45 numbers after nine, such as 10, 11, 12, and so forth.

So 45th number will be 10+(45–1)*1=54

Therefore, this large number's final four digits will be 5354.

Now 5354 mod 16= 10

So remainder will be 10

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