a positive no.n when divided by 35 gives the remainder 3. what will be the remainder when this no. is divided by 7
Answers
Answer:
Step-by-step explanation:
The remainder will still be 3.
The original number must be of the form n = 35d+3, that is, 35 goes into this number d times and gives a remainder r of 3. When you divide n by 7, you can see that n = 7(5d) +3, so that 7 goes into n 5d times and leaves a remainder of 3.
What about the reverse question? If a number n, when divided by 7 gives a remainder of 3, must the remainder still be 3 when n is divided by 35?
No. Consider the numbers 10, 17, 24, 31, 38, 45, 52, etc, each number exactly 7 more than the previous number. When each is divided by 7, the remainder is 3. However, when you divide each of these numbers by 35, the remainders are 10, 17, 24, 31, 3, 10, 17, etc. Thus if a number gives a remainder of 3 when divided by 7, when it is divided by 35, its remainder could be 3, 10, 17, 24, or 31 — all of which give remainders of 3 when divided by 7.