Question

HELLO BRAINLY WASIYO❤❤...XD

HERE'S YOUR QUESTION: -☺️

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.

❌❌DON'T SPAM!!!!❌❌
​

Answer 1

$\huge\sf\underline{\underline{Solution:}}$

▪Given that:-

• Number = 4n
• N is a natural number.

▪To check:-

• Value of n which ends with zero

______________________________________

Take an example of a number which ends with 0 (zero).

15 × 2 = 30

2 × 5 = 10

30 × 2 = 60

As we know that from above examples number ending with zero has both 2 and 5 as their prime factors.

Whereas ,

$\tt\bold{4 {}^{n} = (2 \times 2) {}^{n}}$

It does not have 5 as a prime factor

So, it does not end with zero.

•°• 4^n cannot end with zero for any natural number n.

Answer 2

Answer:

Step-by-step explanation:

To Check :-

Any value of n for which 4n ends with the digit zero.

Solution :-

Let $\sf 4^n$ ends with 0.

Therefore, $\sf 4^n$ is divided by 2 and 5.

Prime factors = 2 × 2

$\sf\implies 4^n=(2\times2)^n=2^2^n$

Thus, Prime factorization of $\sf 4^n$ does not contain 5.

Therefore, the fundamental theorem of arithmetic guarantees that there is no other factor of $\sf 4^n$.

Hence, there is no natural number n for which $\bf 4^n$ ends with digit 0.