Question

Find the remainder when 7^187 is divided by 800

Answer 1

Answer: 343

Step-by-step explanation: In first go, this question looks quite complicated but that isn’t the case. The thumb rule in questions where you have to find out the remainder of [a^n / d] is to try and think of a power of ‘a’ that is close to a multiple of d

Here, we know that 7^4 = 2401 = 3*800 + 1

This means that 7^4 when divided by 800 will leave a remainder of 1

=> 7^(multiple of 4) when divided by 800 will leave a remainder of 1

=> 7^184 when divided by 800 will leave a remainder of 1

We know that 7^187 = 7^3 * 7^184 = 343 * 7^184

We need to find out the remainder of 7^187 when divided by 800. We know that 7^184 will leave a remainder of 1 and 343 will leave a remainder of 343

=> 7^187 when divided by 800 will leave a remainder of 343