Question

Find the remainder when 44^66 is divided by 10​

Answer 1

Answer:

remainder 4

Explanation:

Answer 2

Given:

A number in exponential form$44^{66}$.

To Find:

The remainder when the above number is divided by 10.

Solution:

The given problem can be solved using the concepts of divisibility rules.

1. For a number to be divisible by 10, the units digit must be 0 in all the cases.

2. The value of the remainder when a number is divided by 10 is the value of the units digit of the number.

• For example, the number 12345 when divided by 10 gives the remainder as 5.

3. The value of remainder when$44^{66}$ is divided by 10 is equal to the units digit of$44^{66}$,

=> Units digit of$44^{66}$ =$(40+4)^{66}$,

=> The units digit of $40^{66}$ is zero,

4. The units digit of$4^1$ is 4, the Units digit of 4² is 6, the Units digit of 4³ is 4. For odd values of the exponent, the units digit is 4, For even values of the exponent, the units digit is 6. Therefore, the units digit of 4^66 is 6.

5. Therefore, the units digit of the expression$44^{66}$ is 6. Hence the remainder will be 6.

Therefore, the remainder when 44^66 is divided by 10 will be 6.