Question

Number of even factors of number 1080 is?
1. 24
2. 26
3. 28
4. 30

Answer 1

Correct Answer - Option 1 : 24

Calculation:

By factorisation,

1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5

⇒ 1080 = 2³ × 3³ × 5

To be an even factor it should have either 2¹, 2² or 2³ (three possibilities)

∴ number of even factors = 3 × (3 + 1) × (1 + 1)

⇒ 3 × 4 × 2 = 24

If N = a^p × b^q × c^r, then number of factors of N will be (p + 1)(q +1)(r + 1).

Sum of the factors will be given by (a⁰ + a¹ +......+ a^p)(b⁰ + b¹ + .....+ b^q)(c⁰ + c¹ + ......+ c^r)

Product of all factors = N^{Number of factors/2}