Answer :
We want to divide [tex]$3157$[/tex] by [tex]$77$[/tex]. The goal is to find the quotient [tex]$q$[/tex] and the remainder [tex]$r$[/tex] such that
[tex]$$
3157 = 77 \times q + r \quad \text{with} \quad 0 \le r < 77.
$$[/tex]
Step 1. Estimate a possible quotient by multiplying 77 by a number close to the expected result. Notice that
[tex]$$
77 \times 40 = 3080.
$$[/tex]
Step 2. Since [tex]$3080$[/tex] is close to [tex]$3157$[/tex], try incrementing the multiplier by 1:
[tex]$$
77 \times 41 = 3157.
$$[/tex]
Step 3. Since the product is exactly [tex]$3157$[/tex], we have found that
[tex]$$
3157 = 77 \times 41 + 0.
$$[/tex]
Thus, the quotient is [tex]$41$[/tex] and the remainder is [tex]$0$[/tex].
Final Answer: The result of the division is [tex]$$41 \text{ with a remainder of } 0.$$[/tex]
[tex]$$
3157 = 77 \times q + r \quad \text{with} \quad 0 \le r < 77.
$$[/tex]
Step 1. Estimate a possible quotient by multiplying 77 by a number close to the expected result. Notice that
[tex]$$
77 \times 40 = 3080.
$$[/tex]
Step 2. Since [tex]$3080$[/tex] is close to [tex]$3157$[/tex], try incrementing the multiplier by 1:
[tex]$$
77 \times 41 = 3157.
$$[/tex]
Step 3. Since the product is exactly [tex]$3157$[/tex], we have found that
[tex]$$
3157 = 77 \times 41 + 0.
$$[/tex]
Thus, the quotient is [tex]$41$[/tex] and the remainder is [tex]$0$[/tex].
Final Answer: The result of the division is [tex]$$41 \text{ with a remainder of } 0.$$[/tex]
