Question

Check whether 8n can end with the digit 0 for any n£n

Answer 1

Hey!

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Hey!

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Let us think of some numbers which end the digit 0

10 = 5 × 2

100 = 2 × 2 × 5 × 5

Many more...

Now, Clearly we can see that numbers ending with 0 has prime factors as 2 and 5, take any number ending with digit 0 , it will do have 2 and 5 as a factor.

But,

8^n = (4 × 2) ^n

It doesn't have 5 as it's factor thus 8^n cannot end with zero for any natural number n.

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Hope it helps...!!!

Answer 2

Hey!

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>A number ends with 0 only when the Prime factorization has a common factor 2 and 5.

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•Prime factorization of 8 = 2 × 4

=> 8^n = (2 × 4)^n

•In this we don't have 5 so it will not end with 0

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Regards :)

Cybary

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