Exercise · ZW-MULTIPLICATION-PRINCIPLE-010 · ★★★ Advanced
How many positive divisors does 360 have? Use \(360=2^3\cdot 3^2\cdot 5\).
Choose one option.
Show answer
- C. \(24\)
Explanation
A divisor is \(2^a3^b5^c\) with \(0\le a\le 3\), \(0\le b\le 2\), \(0\le c\le 1\): \(4\cdot 3\cdot 2=24\) choices.
Review the concept: Multiplication principle
If a task is done in successive steps and step \(i\) admits \(n_i\) options regardless of how the earlier steps were done, the total number of ways \(N\) is the product of those numbers.
\[N=n_1\cdot n_2\cdots n_k\]
More practice problems: multiplication principle
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- ZW-MULTIPLICATION-PRINCIPLE-004 How many three-digit numbers (100 to 999) have three distinct digits?
- ZW-MULTIPLICATION-PRINCIPLE-005 A plate has 3 different letters (out of 26) followed by any 2 digits. How many plates are there?
- ZW-MULTIPLICATION-PRINCIPLE-006 How many functions are there from a 4-element set to a 3-element set?
- ZW-MULTIPLICATION-PRINCIPLE-007 How many even three-digit integers (100 to 999) are there?
- ZW-MULTIPLICATION-PRINCIPLE-008 Select the condition required to multiply the number of options of each step.