The remainder when 7^403 is divided by 100.
Please give me two methods so that i can comply please hurry i have a test tomorrow!
The remainder when 7^403 is divided by 100.
Please give me two methods so that i can comply please hurry i have a test tomorrow!
Hey there, there’s a very easy way solving such question…that’s about finding out the sequence.
let’s see…
7^1 by 100 leaves a remainder of 7.
7^2 by 100 leaves a remainder of 49.
7^3 by 100 leaves a remainder of 43.
7^4 by 100 leaves a remainder of 1.
7^5 by 100 leaves a remainder of 7.
7^6 by 100 leaves a remainder of 49.
.
.
.
now…we have a repeating sequence with us, where the remainder is repeating for every 4 number’s…that’s 7^1 and 7^5 leaves the same remainder….
so remainder of 7^403 will be same as 7^3(since reminder repeats for every 4 numbers;400 is a multiple of 4,so 400+3 came equalent to 3rd term in series)
so remainder is 43
only know aboout this method.no idea about other methods.this is simple and easy to follow
Hey there, there’s a very easy way solving such question…that’s about finding out the sequence.
let’s see…
7^1 by 100 leaves a remainder of 7.
7^2 by 100 leaves a remainder of 49.
7^3 by 100 leaves a remainder of 43.
7^4 by 100 leaves a remainder of 1.
7^5 by 100 leaves a remainder of 7.
7^6 by 100 leaves a remainder of 49.
.
.
.
now…we have a repeating sequence with us, where the remainder is repeating for every 4 number’s…that’s 7^1 and 7^5 leaves the same remainder….
so remainder of 7^403 will be same as 7^3(since reminder repeats for every 4 numbers;400 is a multiple of 4,so 400+3 came equalent to 3rd term in series)
so remainder is 43
only know aboout this method.no idea about other methods.this is simple and easy to follow
