Question

What is the remainder when 7^2001 is divided by 5

Answer 1

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Answer 2

Given:

A number in the exponential form$7^{2001}$ is divided by 5.

To Find:

The remainder when the above number is divided by 5.

Solution:

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

1. The given number is$7^{2001}$.

2. For a number to be divisible by 5, the units digit must be either 0 (OR) 5.

3. The units digit of 7^n is,

• 7 for 4n + 1 type values,
• 9 for 4n + 2 type values,
• 3 for 4n + 3 type values,
• 1 for 4n type values.

4. The power 2001 can be also written as,

=> 2001 = 4(500) + 1,

=> It is of the type 4n + 1, hence the units digit is 7.

5. The remainder when the number 7 is divisible by 5 is 2. As 7 = 5(1) + 2.

Therefore, the remainder when 7^2001 is divided by 5 is 2.