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A number is given: $1234513151313653211415515253$

Is there any way to find out the reminder when it divided by 8? What will be happened if I use MOD rules here?

Marc van Leeuwen
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user2378
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2 Answers2

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When you divide by $8$, you only need to worry about the last 3 numbers. So $1234513151313653211415515253$ mod $8$ becomes $253$ mod $8$. Now it's a cake walk!

Rocket Man
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  • why last three digits only essential? – user2378 Nov 02 '13 at 15:56
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    We know that $8$ goes into $1000$. That means that any number that ends with $000$ such as $123234000$ will be divisible by $8$. Therefore, we only need to check the last $3$ numbers.

    For instance, we can write $1234513151313653211415515253$ as $1234513151313653211415515000+253$. Since $8$ goes into $1234513151313653211415515000$, we only have to check $253$.

     – Rocket Man Nov 02 '13 at 16:00
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It suffices to look at the last 3 digits. Hence remainder is $253 \mod 8 = 5$

meta_warrior
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