find remainder when 2^1000 when divided by 13
Answers
Answer:
So, when 2 is divided by 13, the remainder is 2. (2 = 0*13 + 2). This remainder of 2 is then multiplied. 2^1000 is a massive number.
Answer:
Remainder is 3
Step-by-step explanation:
In any remainder question, play smart by trying to express the dividend in the form of (divisor + 1) or (divisor – 1) (as far as you can) so that the remainder turns out to be 1. Apart from this, use the following shortcuts to find out remainders for large values:
Remainder = Remainder + Remainder
Remainder = Remainder * Remainder
The above concepts can be extended to the sum or product of any number of values.
Also, when you write the dividend (which has a power) in the form of , the remainder will always be 1. However, if you write the same dividend as , the remainder will be 1 if the power is even and will be -1 if the power is odd. Since the remainder cannot be negative, we add the divisor to the negative remainder to obtain the final remainder.
Let us now try and apply these concepts to the problem at hand.
By writing down the first few powers of 2, we observe that i.e. 64 is the number we can write in the form of (13k -1).
Therefore, can be written as () * (). So,
Remainder = Remainder * Rem.
Let’s now calculate the individual remainders.
Remainder :
= = .
So, here, we have written the dividend, in the form of , where 13 is the divisor. As discussed earlier, since the power is even, the remainder here will be 1.
Remainder = Remainder= 3.
Therefore, final remainder = 1 * 3 = 3.