Perform the modular arithmetic
7mod3+5mod8-32mod5
Determine 7 mod 3Define modulus:
Remainder of a ÷ b
In this case, a = 7 and b = 3
Calculate whole number part:
3 goes into 7 a total of 2 times
3 x 2 = 6
Calculate remainder part:
Remainder = a - whole number
Remainder = 7 - 6
7 mod 3 ≡ 1
This means that 3 does not divide 7 → 3∤7
This means that 3 does not divide 7 → 3∤7
Excel or Google Sheets formula:
Excel or Google Sheets formula:=MOD(7,3)Determine 5 mod 8
Define modulus:
Remainder of a ÷ b
In this case, a = 5 and b = 8
Calculate whole number part:
8 goes into 5 a total of 0 times
8 x 0 = 0
Calculate remainder part:
Remainder = a - whole number
Remainder = 5 - 0
5 mod 8 ≡ 5
This means that 8 does not divide 5 → 8∤5
This means that 8 does not divide 5 → 8∤5
Excel or Google Sheets formula:
Excel or Google Sheets formula:=MOD(5,8)Determine -32 mod 5
Define modulus:
Remainder of a ÷ b
In this case, a = -32 and b = 5
Calculate whole number part:
5 goes into -32 a total of -7 times
5 x -7 = -35
Calculate remainder part:
Remainder = a - whole number
Remainder = -32 - -35
-32 mod 5 ≡ 3
This means that 5 does not divide -32 → 5∤-32
This means that 5 does not divide -32 → 5∤-32
Excel or Google Sheets formula:
Excel or Google Sheets formula:=MOD(-32,5)Final Answer:
1 + 5 + 3 = 9
What is the Answer?
-32 mod 5 ≡ 3
This means that 5 does not divide -32 → 5∤-32
This means that 5 does not divide -32 → 5∤-32
How does the Modulus Calculator work?
Free Modulus Calculator - Given 2 integers a and b, this modulo calculator determines a mod b or simplifies modular arithmetic such as 7 mod 3 + 5 mod 8 - 32 mod 5
This calculator has 1 input.
This calculator has 1 input.
What 1 formula is used for the Modulus Calculator?
amodb = Remainder after a ÷ b
What 2 concepts are covered in the Modulus Calculator?
- modulus
- the remainder of a division, after one number is divided by another.
a mod b - remainder
- The portion of a division operation leftover after dividing two integers
