Answer :
To find the remainder when dividing [tex]$181$[/tex] by [tex]$6$[/tex], we can use the division algorithm. The division algorithm states that for any integers [tex]$a$[/tex] (dividend) and [tex]$b$[/tex] (divisor, with [tex]$b > 0$[/tex]), there exist unique integers [tex]$q$[/tex] (quotient) and [tex]$r$[/tex] (remainder) such that
[tex]$$
a = b \times q + r \quad \text{with} \quad 0 \leq r < b.
$$[/tex]
For this problem, [tex]$a = 181$[/tex] and [tex]$b = 6$[/tex].
### Step 1: Find the Quotient
Divide [tex]$181$[/tex] by [tex]$6$[/tex] to determine how many whole times [tex]$6$[/tex] fits into [tex]$181$[/tex]. The integer part of the division is
[tex]$$
q = \lfloor 181 \div 6 \rfloor = 30.
$$[/tex]
This means [tex]$6$[/tex] goes into [tex]$181$[/tex] exactly [tex]$30$[/tex] times.
### Step 2: Calculate the Remainder
Next, we use the quotient to calculate the remainder:
[tex]$$
r = 181 - 6 \times 30.
$$[/tex]
Calculate [tex]$6 \times 30$[/tex]:
[tex]$$
6 \times 30 = 180.
$$[/tex]
Then subtract:
[tex]$$
r = 181 - 180 = 1.
$$[/tex]
### Final Answer
The remainder when [tex]$181$[/tex] is divided by [tex]$6$[/tex] is
[tex]$$
\boxed{1}.
$$[/tex]
[tex]$$
a = b \times q + r \quad \text{with} \quad 0 \leq r < b.
$$[/tex]
For this problem, [tex]$a = 181$[/tex] and [tex]$b = 6$[/tex].
### Step 1: Find the Quotient
Divide [tex]$181$[/tex] by [tex]$6$[/tex] to determine how many whole times [tex]$6$[/tex] fits into [tex]$181$[/tex]. The integer part of the division is
[tex]$$
q = \lfloor 181 \div 6 \rfloor = 30.
$$[/tex]
This means [tex]$6$[/tex] goes into [tex]$181$[/tex] exactly [tex]$30$[/tex] times.
### Step 2: Calculate the Remainder
Next, we use the quotient to calculate the remainder:
[tex]$$
r = 181 - 6 \times 30.
$$[/tex]
Calculate [tex]$6 \times 30$[/tex]:
[tex]$$
6 \times 30 = 180.
$$[/tex]
Then subtract:
[tex]$$
r = 181 - 180 = 1.
$$[/tex]
### Final Answer
The remainder when [tex]$181$[/tex] is divided by [tex]$6$[/tex] is
[tex]$$
\boxed{1}.
$$[/tex]
