When a positive integer K is divided by 6, the remainder is 1, what is the remainder when 5K is divided by 3?
3 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
When K divide by 6 , the rmainder = 1
==> we can write the equation:
k/6 = n + 1 where n is an integer.
Now multiply by 6:
==> k = 6n + 6
Now multiply by 5:
==> 5k = 30n + 30
Now divide by 3:
==> 5k/3 = 30/3n + 30/3
==> 5k/3 = 10n + 10
But 10 >3 , then the remainder should be less <3
The remainder is either 1 or 2.
Let us rewrite 10 as multiply of 3.
==> 5k/3 = 10n + 3*3 + 1
==> 5K/3 = 10N+9 + 1
Since 10n+10 is an integer , then the remainder is 1:
william1941 | College Teacher | (Level 3) Valedictorian
When K is divided by 6 the remainder is 1.
We can therefore write K as 6a+1, where a is a whole number.
Now 5K can be written as 5*(6a+1)=30a+5
When 5K is divided by 3 it is the same as dividing (30a+5) by 3 or (30a+5/3 which is equal to 10a+5/3. Now 10a is a whole number, 5/3 can be written as 1+ 2/3.
Therefore 5K/3= 10a +1+ 2/3.
Therefore the remainder is 2.
The required answer is 2.
neela | High School Teacher | (Level 3) Valedictorian
When K is divided by 6, remainder is 1.
So K = 6n+1.
Therefore 5K = 6(n*5) +5we get a remainder 5.
5k = 3*(2*n*5) + 3+2
5 k = 3 (10n+1)+2.
Therefore 5k / 3 = (10n+1) is quotient and Remainder = 2.