Single correct option
How many even positive divisors does 720 have?
- A. 20
- B. 24
- C. 18
- D. 30
Show answer and solution
Answer: (B) 24
720 = 2⁴ × 3² × 5.
Total divisors = (4 + 1)(2 + 1)(1 + 1) = 30.
Odd divisors use no factor of 2: (2 + 1)(1 + 1) = 6.
Even divisors = 30 − 6 = 24. (Directly: choose the power of 2 from 1 to 4 — 4 ways — times 3 × 2 = 24.)
30 is the total number of divisors, a trap for those who skip the 'even' condition.
Total divisors = (4 + 1)(2 + 1)(1 + 1) = 30.
Odd divisors use no factor of 2: (2 + 1)(1 + 1) = 6.
Even divisors = 30 − 6 = 24. (Directly: choose the power of 2 from 1 to 4 — 4 ways — times 3 × 2 = 24.)
30 is the total number of divisors, a trap for those who skip the 'even' condition.
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