how to find the value of modulus
Answers
When you see "modulo", especially if you are using a calculator, think of it as the remainder term when you do division.
Examples:
The result of 10 modulo 5 is 0 because the remainder of 10 / 5 is 0.
The result of 7 modulo 5 is 2 because the remainder of 7 / 5 is 2.
The reason your calculator says 113 modulo 120 = 113 is because 113 < 120, so it isn't doing any division.
More generally, the idea is that two numbers are congruent if they are the same modulo a given number (or modulus)
For example, as above, 7≡2mod57≡2mod5 where 55 is our modulus.
Another issue is that of inverses, which is where the confusion of 1/171/17 comes in.
We say that aa and bb are inverses modulo nn, if ab≡1modnab≡1modn, and we might write b=a−1b=a−1.
For example 17⋅113=1921=120⋅16+1≡1mod12017⋅113=1921=120⋅16+1≡1mod120, so 17−1=11317−1=113 modulo 120120.