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Find the total number of factors of 723 + 722 + 721 + 7201. 1602. 3153. 3254. 120 |
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Answer» Correct Answer - Option 2 : 315 Given: The given number is 723 + 722 + 721 + 720 Concept used: A given natural number can be expressed as 2a.3b.5c.7d...... and so on Where a, b, c, d ...... and so on are whole numbers Total number of factors = (a + 1) × (b + 1) × (c + 1) × (d + 1) ...... and so on Calculation: Given number is 723 + 722 + 721 + 720 The number can be expressed as 720 × (73 + 72 + 71 + 1) The number can be expressed as 720 × (343 + 49 + 7 + 1) = 720 × 400 The number can be expressed as 720 × 24 × 52 Total number of factors = (20 + 1) × (4 + 1) × (2 + 1) Total number of factors = 21 × 5 × 3 = 315 ∴ Total number of factors is 315 |
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