Correct Answer - Option 1 : 7
Concept:
Unit digit: It is defined as the digit at once place of a given number. To calculate the unit digit, of a certain number with some power or product of numbers, we only have to focus on the digit at the one place of numbers.
Cyclicity: The concept of cyclicity is used to identify the last digit of the number. The cyclicity of any number is about the last digit and how they appear in a certain defined manner.
Procedure to find unit digit:
Step-1: Take the given power like the power of the unit digit of a given number.
Step-2: Divide the power by cyclicity of a given number
- If it is completely divisible, then the unit digit will be digit at once place to the power its cyclicity.
- If it is not divisible completely, replace the power with the remainder obtained, let xy (where x is a unit digit of a given number and y is remainder).
Step-3: Now, the unit digit will be obtained by simplifying xy.
Calculation:
Given term is 457 + 675 × 64
The cyclicity of 5, 7, and 6 is 1, 4, and 1 respectively.
Hence every power of 5 and 6 gives 5 and 6 as a unit digit.
For 675, as mentioned in step 1, we can write it as 75.
On deviding the power 5 by cyclicity of 7 which is 4, we will get 7 as a unit digit.
Hence unit digit of a term will be unit digit of 5 + 7 × 6
= 47
This shows unit digit is 7.
| Number (n) |
Unit digit of n1 |
Unit digit of n2 |
Unit digit of n3 |
Unit digit of n4 |
Cyclicity |
| 0 |
0 |
0 |
0 |
0 |
1 |
| 1 |
1 |
1 |
1 |
1 |
1 |
| 2 |
2 |
4 |
8 |
6 |
4 |
| 3 |
3 |
9 |
7 |
1 |
4 |
| 4 |
4 |
6 |
4 |
6 |
2 |
| 5 |
5 |
5 |
5 |
5 |
1 |
| 6 |
6 |
6 |
6 |
6 |
1 |
| 7 |
7 |
9 |
3 |
1 |
4 |
| 8 |
8 |
4 |
2 |
6 |
1 |
| 9 |
9 |
1 |
9 |
1 |
2 |
