1.

Find the total number of factors of 723 + 722 + 721 + 7201. 1602. 3153. 3254. 120

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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