Use the Division Algorithm (and no decimals!) to answer the following questions.
ID: 3120307 • Letter: U
Question
Use the Division Algorithm (and no decimals!) to answer the following questions.
Does 17 | 207?
Does 17 | 204?
Does 17 = 23 mod 6?
The time is 9:45. What time will it be in 2411 minutes? Your answer must involve use of the Division Algorithm mod 60. Don't worry about am/pm.
Important
Recall from class that the best way to show work in Modular Arithmetic is by use of The Division Algorithm. Unfortunately you can get through the Connect work without doing this. The way you use this is as follows:
Q: What is (-17) mod 5?
A: Write -17 = 5* quotient + remainder
where the first blank is the quotient and the second is the positive remainder 0r< 5.
So, -17 = 5*(-4) + 3
It follows that -17 3 mod 5, or as CS people like to write it -17 mod 5 = 3.
Explanation / Answer
A) 17 does not divide 207 as207 is congruent to 3 mod 17 i.e. 207 when divided by 17 leaves 3 as remainder.
B) 17 divides 204 as 204 is congruent to 0 mod 17. Yes 17 is congruent to 23 mod 6 as 17-23 =-6 /6 . Hence true .
2411is congruent to 11 mod(60) . Hence time will be 1:56.
As 2411 = 60×40 + 11
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