It's called modular arithmetic. Look it up. It's quite useful, and will open you up to some interesting mathematics.
Hi all, I am Chaitanya, I am preparing for GRE, unfortunately I am poor at mathematics. But with some help I can understand quickly.
I came across few questions, solved few on mu own. But I came across one question,
What is the remainder of the division of 14414*14416*14418 by 14?
Is there any easy way to solve this?
Thank you all in advance and sorry if I ask a very silly question.
Yes, and you should start by looking at the first hit.
modular arithmetic - Google Search
CB
I am reading from this page.
I dint understood this para.
Can anyone explain? Thanks in advance.Modular arithmetic lets us state these results quite precisely, and it also provides a convenient language for similar but slightly more complex statements. In the above example, our modulus is the number 2. The modulus can be thought of as the number of classes that we have broken the integers up into. It is also the difference between any two "consecutive" numbers in a given class.
we have to find the solution of the eqn
x≡14414*14416*14418 (mod 14)
When 14414 is divided by 14 , it leaves remainder as 8,
14416 is divided by 14, it leaves remainder as 10,
14418 is divided by 14, it leaves remainder as 12.
so we get
14414*14416*14418≡ 8*10*12≡80*12≡10*12≡8(mod 14)
Hence,
the remainder is 8 when 14414*14416*14418 is divided by 14.
i think this will help.but please check the calculations
Thanks dude. I thought the answer would be 3. In the page I was reading(this) the author was describing about congruency for addition and multiplication. I thought for division
0/0≡1mod2
0/1≡0mod2
1/0≡0mod2
1/1≡1mod2
Since even*even*even/even is even/even and 0/0≡1mod2, I thought answer is 3. Since the options given were
8
3
12
10
6
Since 3 is the only odd number I thought 3 would be the right answer. How ever there is little confusion in your post. How did you exactly said that 8 is the right answer. It can be either 10 or 12. Could you please explain.
Thank you in advance