check whether 4n can end with the digit zero for any natural number n.
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Answered by
22
here according to question...
4n=(5*2) {because to end with zero.. a no. must be a multiple of 5 and 2}
so.. 4n can be written as 2*2n
that gives.- 2*2n=5*2
cancelling 2 on both sides will give you the answer that unless n is not equal to a multiple of 5, till then, 4n will not end with a zero
4n=(5*2) {because to end with zero.. a no. must be a multiple of 5 and 2}
so.. 4n can be written as 2*2n
that gives.- 2*2n=5*2
cancelling 2 on both sides will give you the answer that unless n is not equal to a multiple of 5, till then, 4n will not end with a zero
Answered by
23
Step-by-step explanation:
→ No, 4ⁿ can never end with the digit 0 for any natural number n .
→ If 4ⁿ ends with 0 then it must have 5 as a factor .
But, 4ⁿ = ( 2² )ⁿ = 2²ⁿ .
→ It shows that 2 is the only prime factor of 4ⁿ .
Also, we know from the fundamental theorem of airthematic that the prime factorisation of each number is unique .
So, 5 is not a factor of 4ⁿ .
Hence, 4ⁿ can never end with the digit 0 .
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