Question

what is the remainder when 7 to the power 63 is divided by 344​

Answer 1

Answer: 343

Step-by-step explanation:

Powers of 7 are cyclical after every 4 powers ie.

7¹ - 7

7² - 49

7³ - 343

7⁴ - 2401

Now you can clearly see that after that since 2401 ends with 7 multiplying it would give a number that ends with 7, the next one would end with 49 and so on,

Hence 63 can be expressed as (15×4)+ 3 , ie. after 7⁶⁰ only 3 powers of 7 will be left

7⁽¹⁵ˣ⁴⁾⁺³ therefore the therefore only 7³ = 343 extra would need to be divided by 344 and thus the answer is 343/344 so the remainder is 343

Answer 2

The answer is b) 343

Step-by-step explanation:

First, let us take the exponents to 7 and find the results:

$7^1 = 7$

$7^2 = 49$

$7^3 = 343$

Now, 343 is one less than 344. So, if we would divide 343 by 344, the remainder would be 343 only.

Also, if we see $7^{63} = (7^3)^{21$

So, every time we would divide $7^3$ we would be left with 343 as the remainder.

Hence, the answer should be 343.