Question

When the integer n is divided by 8, the remainder is 3. what is the remainder if 6n is divided by 8?

Answer 1

Heya User,

Modular Arithmetic ^_^

--> Euclid's lemma holds a proper claim here.. ^_^

--> n = 8k + 3  --> [ By Euclid's lemma ]
--> 6n = 6 ( 8k + 3 )
           = 48k + 18

--> 6n = 8 [ 6k + 2 ] + 2

Hence, 6n = 8a + 2  √√

This implies that the remainder on dividing 6n with 8 is '2'.

Answer 2

Given,

when the integer n is divided by 8 then the remainder is 3.

To Find,

the remainder if 6n is divided by 8.

Solution,

when n is divided by 8, we get

n = 8q + 3   (here, 3 is remainder)              (1)

now, multiply 6 on both sides

6n = 48q + 18

6n = 48q + 16 + 2

6n = 8(6q + 2) + 2

6m = 8m + 2   ( where, m = 6q + 2)

Hence the remainder on dividing 6n by 8 is 2.