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Answer :
To solve the problem, we need to determine which division leaves a remainder of [tex]$59$[/tex]. We are given four divisions:
[tex]$$1936 \div 94,\quad 1937 \div 94,\quad 1938 \div 94,\quad \text{and} \quad 1939 \div 94.$$[/tex]
The remainder when a number [tex]$N$[/tex] is divided by [tex]$94$[/tex] is given by
[tex]$$N = 94 \times q + r,$$[/tex]
where [tex]$q$[/tex] is the quotient (an integer) and [tex]$r$[/tex] is the remainder (with [tex]$0 \le r < 94$[/tex]).
Let's go step by step.
1. For [tex]$1936 \div 94$[/tex], let the remainder be [tex]$r_1$[/tex]. When we perform the division, we find:
[tex]$$r_1 = 56.$$[/tex]
(This means [tex]$1936 = 94 \times q_1 + 56$[/tex] for some integer [tex]$q_1$[/tex].)
2. For [tex]$1937 \div 94$[/tex], let the remainder be [tex]$r_2$[/tex]. When we perform the division, we obtain:
[tex]$$r_2 = 57.$$[/tex]
(So [tex]$1937 = 94 \times q_2 + 57$[/tex] for some integer [tex]$q_2$[/tex].)
3. For [tex]$1938 \div 94$[/tex], let the remainder be [tex]$r_3$[/tex]. When we perform the division, we find:
[tex]$$r_3 = 58.$$[/tex]
(Thus [tex]$1938 = 94 \times q_3 + 58$[/tex] for some integer [tex]$q_3$[/tex].)
4. For [tex]$1939 \div 94$[/tex], let the remainder be [tex]$r_4$[/tex]. When we perform the division, we have:
[tex]$$r_4 = 59.$$[/tex]
(So [tex]$1939 = 94 \times q_4 + 59$[/tex] for some integer [tex]$q_4$[/tex].)
Since we are looking for the division that yields a remainder of [tex]$59$[/tex], we see that:
[tex]$$r_4 = 59.$$[/tex]
Thus, the division that leaves a remainder of [tex]$59$[/tex] is
[tex]$$1939 \div 94.$$[/tex]
Therefore, the answer is [tex]$\boxed{1939}$[/tex].
[tex]$$1936 \div 94,\quad 1937 \div 94,\quad 1938 \div 94,\quad \text{and} \quad 1939 \div 94.$$[/tex]
The remainder when a number [tex]$N$[/tex] is divided by [tex]$94$[/tex] is given by
[tex]$$N = 94 \times q + r,$$[/tex]
where [tex]$q$[/tex] is the quotient (an integer) and [tex]$r$[/tex] is the remainder (with [tex]$0 \le r < 94$[/tex]).
Let's go step by step.
1. For [tex]$1936 \div 94$[/tex], let the remainder be [tex]$r_1$[/tex]. When we perform the division, we find:
[tex]$$r_1 = 56.$$[/tex]
(This means [tex]$1936 = 94 \times q_1 + 56$[/tex] for some integer [tex]$q_1$[/tex].)
2. For [tex]$1937 \div 94$[/tex], let the remainder be [tex]$r_2$[/tex]. When we perform the division, we obtain:
[tex]$$r_2 = 57.$$[/tex]
(So [tex]$1937 = 94 \times q_2 + 57$[/tex] for some integer [tex]$q_2$[/tex].)
3. For [tex]$1938 \div 94$[/tex], let the remainder be [tex]$r_3$[/tex]. When we perform the division, we find:
[tex]$$r_3 = 58.$$[/tex]
(Thus [tex]$1938 = 94 \times q_3 + 58$[/tex] for some integer [tex]$q_3$[/tex].)
4. For [tex]$1939 \div 94$[/tex], let the remainder be [tex]$r_4$[/tex]. When we perform the division, we have:
[tex]$$r_4 = 59.$$[/tex]
(So [tex]$1939 = 94 \times q_4 + 59$[/tex] for some integer [tex]$q_4$[/tex].)
Since we are looking for the division that yields a remainder of [tex]$59$[/tex], we see that:
[tex]$$r_4 = 59.$$[/tex]
Thus, the division that leaves a remainder of [tex]$59$[/tex] is
[tex]$$1939 \div 94.$$[/tex]
Therefore, the answer is [tex]$\boxed{1939}$[/tex].
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