Question : What will be the remainder when $252^{126}+244^{152}$ is divided by 10?
Option 1: 4
Option 2: 6
Option 3: 0
Option 4: 8
Correct Answer: 0
Solution :
To find the remainder when $252^{126}+244^{152}$ is divided by 10, we only need to consider the unit digit of each term in the sum.
The unit digit of $252^{126}$ is the same as the unit digit of 2
126
.
Divide 126 by 4 and get remainder = 2
So, the unit digit of $252^{126}$ is $2^2$ = 4
The unit digit of $244^{152}$ is the same as the unit digit of 4
152
.
If the power of 4 is even, the unit digit is 6.
So, the unit digit of $244^{152}$ is 6.
The sum of the unit digits = 4 + 6 = 10
The remainder when $252^{126}+244^{152}$ is divided by 10 = Remainder when 10 is divided by 10 = 0
So, the remainder is 0.
Hence, the correct answer is 0.
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