Math challenge #1 - Find the remainder!
Question
(Difficulty: 4/10)
What is the remainder of 1111....1 (a total of 2017 '1' s) divided by 12?
Let's see who can get the answer first! Remember to show your steps :)
Solution
A number is divisible by 12 if it is divisible by 3 and 4.
Method of checking if a number is divisible by 3: Sum up all its digits and see if it is divisible by 3.
Method of checking if a number is divisible by 4: See if the number formed by the last 2 digits are divisible by 4.
Therefore, the closest number is 111...1116.
Because the sum of digits is 2022, which is divisible by 3; and its final 2 digits is 16, which is divisible by 4.
Therefore the remainder is 7.
congrats to @mathfortress and @happychau123 for getting the correct answer!
My solution is the same as @happychau123 's and this method does not require calculator at all! Great job!
So a short summary:
A number is divisible by 12 if it is divisible by 3 and 4.
Method of checking if a number is divisible by 3: Sum up all its digits and see if it is divisible by 3.
Method of checking if a number is divisible by 4: See if the number formed by the last 2 digits are divisible by 4.
Therefore, the closest number is 111...1116.
Because the sum of digits is 2022, which is divisible by 3; and its final 2 digits is 16, which is divisible by 4.
Therefore the remainder is 7.
Thank You!
Here is another solution for this:
You can just find the closest number can be divided by 12
In this case 111......116
, hence the reminder is 12-5 = 7
Bingo! This is a good solution
1 mod 12 = 1
11 mod 12 = 11
111 mod 12 = 3
1111 mod 12 = 7
11111 mod 12 = 11
111111 mod 12 = 3
1111111 mod 12 =7
This pattern repeats every time you insert a 1. So 2017 divided by 3 is 672 and a third. So the remainder will be the second number in the pattern in this case 7.
Excellent! 7 is the correct answer
Hi.
Is the answer 1.
No sorry :( Can you show your steps? Let me see how you arrived at 1
I am stumped.
do you need some hints? :)
yup
Do you know how to check if a number is divisible by 3? How about by 4? If a number passes these 2 tests, then it is divisible by 12
A really challenging question... any hints on how to check whether a number is divisible by 12?
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