정수의 조건과 곱셈

문제

두 정수 $A, B$가 다음 조건을 모두 만족한다.

(가) $A$는 음의 정수이고, $B$는 양의 정수이다. (나) $|A| \times B = 108$ 이다. (다) $A+B$는 약수의 개수가 2개인 양의 정수이다.

이때, $A \times B$의 값으로 알맞은 것은?

<!-- Axis Labels -->
<text x="130" y="0" transform="scale(0.5, -0.5)" class="axis-label" dominant-baseline="hanging" text-anchor="end">a = |A|</text>
<text x="-5" y="120" transform="scale(0.5, -0.5)" class="axis-label" dominant-baseline="auto" text-anchor="middle">B</text>
<circle cx="0" cy="0" r="1.5" fill="#1F2937" stroke="none"/>
<text x="-2.5" y="-2.5" transform="scale(0.5, -0.5)" class="tick-label" text-anchor="end">O</text>

<!-- Tick Marks and Labels for X-axis -->
<g class="tick-label" dominant-baseline="hanging" transform="scale(0.5, -0.5)">
  <line x1="10" y1="0" x2="10" y2="-2" stroke="#1F2937"/> <text x="10" y="2" text-anchor="middle">10</text>
  <line x1="20" y1="0" x2="20" y2="-2" stroke="#1F2937"/> <text x="20" y="2" text-anchor="middle">20</text>
  <line x1="30" y1="0" x2="30" y2="-2" stroke="#1F2937"/> <text x="30" y="2" text-anchor="middle">30</text>
  <line x1="40" y1="0" x2="40" y2="-2" stroke="#1F2937"/> <text x="40" y="2" text-anchor="middle">40</text>
  <line x1="50" y1="0" x2="50" y2="-2" stroke="#1F2937"/> <text x="50" y="2" text-anchor="middle">50</text>
  <line x1="60" y1="0" x2="60" y2="-2" stroke="#1F2937"/> <text x="60" y="2" text-anchor="middle">60</text>
</g>
<!-- Tick Marks and Labels for Y-axis -->
<g class="tick-label" text-anchor="end" dominant-baseline="middle" transform="scale(0.5, -0.5)">
  <line x1="0" y1="-10" x2="2" y2="-10" stroke="#1F2937"/> <text x="-2" y="-10">10</text>
  <line x1="0" y1="-20" x2="2" y2="-20" stroke="#1F2937"/> <text x="-2" y="-20">20</text>
  <line x1="0" y1="-30" x2="2" y2="-30" stroke="#1F2937"/> <text x="-2" y="-30">30</text>
  <line x1="0" y1="-40" x2="2" y2="-40" stroke="#1F2937"/> <text x="-2" y="-40">40</text>
  <line x1="0" y1="-50" x2="2" y2="-50" stroke="#1F2937"/> <text x="-2" y="-50">50</text>
  <line x1="0" y1="-60" x2="2" y2="-60" stroke="#1F2937"/> <text x="-2" y="-60">60</text>
  <line x1="0" y1="-70" x2="2" y2="-70" stroke="#1F2937"/> <text x="-2" y="-70">70</text>
  <line x1="0" y1="-80" x2="2" y2="-80" stroke="#1F2937"/> <text x="-2" y="-80">80</text>
  <line x1="0" y1="-90" x2="2" y2="-90" stroke="#1F2937"/> <text x="-2" y="-90">90</text>
  <line x1="0" y1="-100" x2="2" y2="-100" stroke="#1F2937"/> <text x="-2" y="-100">100</text>
</g>

<!-- Line B=a (scaled, 1 unit = 2 pixels) -->
<line x1="0" y1="0" x2="110" y2="110" class="condition-line"/>
<text x="70" y="70" transform="scale(0.5,-0.5)" class="tick-label" text-anchor="end">B = a</text>

<!-- Point where B=a (for context) -->
<!-- sqrt(108) approx 10.39 -->
<circle cx="10.39" cy="10.39" r="1.5" fill="#1F2937" stroke="none"/>
<text x="12" y="10.39" transform="scale(0.5,-0.5)" class="tick-label" text-anchor="start">a=B=√108</text>

<!-- Data Points (a, B) and A+B values -->
<!-- Points where a*B=108 and B > a -->
<!-- (a, B) -->
<circle cx="1" cy="108" r="1.5" class="point"/> <text x="1.5" y="108" transform="scale(0.5, -0.5)" class="sum-label">(1, 108)</text> <text x="2" y="114" transform="scale(0.5, -0.5)" class="prime-label">A+B=107 (소수)</text>
<circle cx="2" cy="54" r="1.5" class="point"/> <text x="2.5" y="54" transform="scale(0.5, -0.5)" class="sum-label">(2, 54)</text> <text x="3" y="60" transform="scale(0.5, -0.5)" class="sum-label">A+B=52</text>
<circle cx="3" cy="36" r="1.5" class="point"/> <text x="3.5" y="36" transform="scale(0.5, -0.5)" class="sum-label">(3, 36)</text> <text x="4" y="42" transform="scale(0.5, -0.5)" class="sum-label">A+B=33</text>
<circle cx="4" cy="27" r="1.5" class="point"/> <text x="4.5" y="27" transform="scale(0.5, -0.5)" class="sum-label">(4, 27)</text> <text x="5" y="33" transform="scale(0.5, -0.5)" class="prime-label">A+B=23 (소수)</text>
<circle cx="6" cy="18" r="1.5" class="point"/> <text x="6.5" y="18" transform="scale(0.5, -0.5)" class="sum-label">(6, 18)</text> <text x="7" y="24" transform="scale(0.5, -0.5)" class="sum-label">A+B=12</text>
<circle cx="9" cy="12" r="1.5" class="point"/> <text x="9.5" y="12" transform="scale(0.5, -0.5)" class="sum-label">(9, 12)</text> <text x="10" y="18" transform="scale(0.5, -0.5)" class="prime-label">A+B=3 (소수)</text>

<!-- Instruction for B < a region -->
<text x="75" y="-15" transform="scale(0.5, -0.5)" class="instruction-text" text-anchor="middle">
    <tspan x="75" dy="0">B &lt; a 인 영역</tspan>
    <tspan x="75" dy="1.2em">A+B = B-a &lt; 0 이므로 조건 (다) 불만족</tspan>
</text>