480 সংখ্যাটির মোট গুণনীয়ক সংখ্যা নির্ণয় করুন।

  1. 12
  2. 24
  3. 48
  4. 36

Answer (Detailed Solution Below)

Option 2 : 24
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Detailed Solution

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প্রদত্ত:

সংখ্যাটি হল 480

অনুসৃত সূত্র:

যদি একটি সংখ্যা N এর উৎপাদক বিশ্লেষণ হয় = ap × bq × cr × ......

তারপর, N এর মোট গুণনীয়ক সংখ্যা = (p + 1) × (q + 1) × (r + 1) × ......

গণনা:

এখানে,

480 এর উৎপাদক বিশ্লেষণ = 25 × 31 × 51

সুতরাং, মোট গুণনীয়ক সংখ্যা = (5 + 1) × (1 + 1) × (1 + 1)

⇒ 6 × 2 × 2

⇒ 24

∴ 480 এর মোট গুণনীয়ক সংখ্যা হল 24

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