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Which of the following regarding prime factors of 360 is not TRUE? A: Total number of factors of 360 is 24. B: Total number of odd factors of 360 is 12. C: Total number of even factors of 360 is 12.

Which of the following regarding prime factors of 360 is not TRUE? A: Total number of factors of 360 is 24. B: Total number of odd factors of 360 is 12. C: Total number of even factors of 360 is 12. Correct Answer Both B and C

GIVEN:

Prime factors of 360 = 2 × 2 × 2 × 3 × 3 × 5

⇒ 23 × 32 × 5

CONCEPT:

Factors of a number

FORMULA USED:

If N = ap × bq × cr × …….

Total factors = (p + 1)(q + 1)(r + 1)

Total odd factors = (q + 1)(r + 1)

Total even factors = p(q + 1)(r + 1)

CALCULATION:

360 = 23 × 32 × 5

Total factors = (3 + 1)(2 + 1)(1 + 1)  = 4 × 3 × 2 = 24

Total odd factors = (2 + 1)(1 + 1) = 3 × 2 = 6

Total even factors = 3(2 + 1)(1 + 1) = 3 × 3 × 2 = 18

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Addition of even factors and odd factors will always be equal to total factors. But even factors will be equal to odd factors will not always be true.

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