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

Solution:

We will use prime factorisation and divisibility rules.

Let us take an example of any positive integer that ends with zero and find its prime factors.

200 = 2 × 2 × 2 × 5 × 5.

Thus, any number that ends with a zero will have 2 and 5 as its prime factors.

Also, any number is divisible by 5 if it ends with zero or 5.

The number 4n can be factored only as (2 × 2)n.

⇒ The prime factorisation of 4n will not have 5 as its factor.

Thus, there is no natural number n for which 4n ends with digit zero

☛ Check: NCERT Solutions for Class 10 Maths Chapter 1

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

Summary:

Thus, there is no value of the natural number n for which 4ⁿ ends with the digit zero

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