Question

show that any number of form 4n nen never end with digit 0

Answer 1

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,

4 ^ n = (2 × 2)^n

It doesn't have 5 as it's factor thus 4^n cannot end with zero for any natural number n.

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Hope it helps...!!!

Answer 2

hey mate

here is the answer

the number end with digit 0 have the prime factors 2^n and 5^n

4^n= (2×2)^n

it have no prime factor 2 but not 5

hence , no of form 4n never end with digit 0

hope it may help

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