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Consider the numbers 4n,where n is …

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Consider the numbers 4n,where n is a natural number.check whether there is any value of n for which 4n ends with the digit zero.

Posted by Anusha_Devisetty Cherry 6 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Shubham Pandey 6 years, 5 months ago

If number is ending with it must end with 0or5but in this case it is ending with power 2

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Sia ? 6 years, 5 months ago

If a number ends with zero then it is divisible by 5.

For unit’s digit to be 0, then 4ⁿ should have 2 and 5 as its prime factors, but 4ⁿ = (2²)ⁿ = 2²ⁿ.

As n {tex}\in{/tex} N we take n=1,2,3,4...etc

So above becomes 4¹,4² ...etc
As it does not contain 5 as one of its prime factors.
Therefore, 4ⁿ will not end with digit 0 for n {tex}\in{/tex} N.

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CBSE > Class 10 > Mathematics