How to quickly calculate the modulus without calculator??

Question

All guys, how to quickly calculate modulus without using calculator, guys. Because Ruby, Python, Php, Java, Java, Javascript, C++, C#, and Other Language, use modulus for some calculations and many also used in " Question Challenge ". So, please tell how 🙏🙏🙏.

Answer 1

Muhammad Akmal Naim you can do this by:

First doing the division such for 47/5 which will only let you go up to 45

Then for 47%5 you do 47-45 which is 3

Answer 2

So basically the modulus function returns the remainder from the euclidian division of two numbers. Example: 15/2=2*7+1 so 15%2=1
Well there's no really a secret to it you have to know very well your multiplication tables but there are some tips and tricks:
-for 2: if the number is even then the remainder will be 0 otherwise 1
-for 5: if the number ends with 0 or 5 the remainder will be 0 otherwise it will ONLY be 1 or 2 or 3 or 4
-for 3: if the sum of the number is divisible by 3 then the remainder will be 0. Example: 123%3=0 because 1+2+3=6 and 6=3*2 or 6%3=0
And there are others but then again, knowing very well your multiplication tables helps a whole lot.

Answer 3

Thanks for answer, Agent. Very helpful

Answer 4

Thanks for answer, David Masabo. Very helpful

Answer 5

Thanks, suggestion Muhammad Hasan.

Answer 6

Once again I thank you for the answer Muhammad Hasan, now i somewhat better understand how to calculate this modulus.

Answer 7

Thanks Haris, for your answer. Very helpful

Answer 8

Thanks, David Masabo, for your answer

Answer 9

Thanks Lisa F, for your answer.

Answer 10

but, how with
10 mod 7 = 3, however, if reversed
7 mod 10 = 7.
or other example
4 mod 3 = 1, however, if reversed
3 mod 4 = 3.
why 7 mod 10 the result remains 7 ??

please, answer Muhammad Hasan and Agent.

Answer 11

Thanks Abenezer Kebede, for your answer.

Answer 12

You can search it in the internet about modulus operation in mathematics, but maybe I'll give some lessons here

Note:
I am telling you how to calculate fastly so I assume you already know the basics of how to find a remainder

In mathematics
a ≡ b (mod c)

means there exist an integer k so that
a = bk+c

so b doesn't necessarily have to be a remainder of a divided by c, but if
b < c then b is called the remainder

example
9 ≡ 1 (mod 2) => 9 = (4)*2+1
but could also be
9 ≡ 3 (mod 2) => 9 = (3)*2+3
9 ≡ 5 (mod 2) => 9 = (2)*2+5
and so on...

Here's some of the fundamental formulas for modulo operation
If a ≡ m (mod c) and b ≡ n (mod c)
then:
1) a+b (mod c) ≡ m+n (mod c)
2) (a*b) (mod c) ≡ (m*n) (mod c)
3) aⁿ (mod c) ≡ mⁿ (mod c)
4) FLT Theorem
If p prime and a is not divisible by p then a^(p-1) (mod p) ≡ a (mod p)
5) Wilson Theorem
Again if p prime then
(p-1)! ≡ p-1 (mod p)

There is also Chinese Remainder Theorem for more faster calculation and many more, but this is already too long

I hope this helps

Answer 13

Because 7 (mod 10)
means
7 = (0)*10+7
so k = 0 in this case
(see the explanation I gave)
and because 7 < 10 so we'll have that 7 is the remainder of 7 divided by 10

Or an easier understanding for remainder is
number = floor(number/divider)*divider+remainder
*learn the function floor to understand more

Answer 14

Here are a few examples

Find
1) 10^2018 (mod 9)
2) 2017*2018*2019 (mod 2016)
3) 2017+2018+2019 (mod 2016)

Answer

1) Because 10 (mod 9) ≡ 1 (mod 9)
we could have
10^2018 (mod 9) ≡ (1)^2018 (mod 9)
≡ 1 (mod 9)
so the remainder is 1

2) It's easy to know that
2017 ≡ 1 (mod 2016)
2018 ≡ 2 (mod 2016)
2019 ≡ 3 (mod 2016)
so
2017*2018*2019 (mod 2016)
≡ (1)*(2)*(3) (mod 2016)
≡ 6 (mod 2016)
so the remainder is 6

3) Coming from number 2 we could have
2017+2018+2019 (mod 2016)
≡ (1)+(2)+(3) (mod 2016)
≡ 6 (mod 2016)
So the remainder is 6

Answer 15

To tell you the truth, for "Question Challenges" you don't need that much understanding, you just have to understand the basic and have some practice

The explanation earlier that I gave is for harder question and maybe for someone who wants to know (If there was :v)

Answer 16

Because you're from Indonesia I have a link where you should study this, it's very recommended 😉
(Non-Indonesians could try also)

Cara mengerjakan soal soal tentang modulo:
https://m.facebook.com/notes/osn-matematika/cara-mengerjakan-soal-soal-tentang-modulo/593356200730155/?refid=18&__tn__=H-R

Answer 17

10 cannot go into 7 so it starts at zero

7 - 0 = 7

this is always the case when they are reversed

Answer 18

No problem

Answer 19

Adi Pratama the C++ modulus operator is ‘%’.

The modulus operator finds the remainder of numbers when a integer devision occurs.

This example takes user input of a number and uses the modulus operatir to find out the remainder when dividing by 3

https://code.sololearn.com/cwNQQOdnYR1o/?ref=app

Answer 20

mod <--> remainder of Euclidean division guys & girls

e.g.
1)
105 % 13 = 1
because 105 = 8 * 13 + 1
2)
2018 % 5 = 3
because 2018 = 403 * 5 + 3
3)
100 % 200 = 100
because 100 = 0 * 200 + 100

wiki on modulo operation:
https://en.m.wikipedia.org/wiki/Modulo_operation