Question

3) What will be the remainder if the number (7) raise to the power 2015 is divided by 25?

a) 1 b) 7 c) 18 d) 24

Answer 1

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Answer 2

Answer: c) 18

Step-by-step explanation:

Since, last digit in different powers of 7,

$7^1 = 7$

$7^2=9$

$7^3=3$

$7^4=1$

$7^5=7$

Hence, if the power of 7 is the multiple of 4 then the last digit of the number = 1,

⇒ $7^{2014}=\text{ 1 is the last digit}$

If we want to find the remainder in a division quickly then we subtract the last digit of the number from the divisor, ( when the divisor is greater than the last digit)

Here,

Number is,

$7^{2015}=7^{2014}\times 7 = 1\times 7$

Hence the last digit of this number is 7,

⇒ Thus, when this digit is divided by 25,

Then remainder = 25 - 7 = 18