How many whole numbers can divide 30 exactly?

a. Eight

To determine how many whole numbers divide 30 exactly, we need to find the divisors of 30. A divisor is a number that divides 30 without leaving a remainder.

First, let's find the divisors of 30 by breaking it down into its prime factorization:

\[
30 = 2 \times 3 \times 5
\]

The divisors of 30 are all possible products of the prime factors \(2\), \(3\), and \(5\) (including 1). These divisors are:

\[
1, 2, 3, 5, 6, 10, 15, 30
\]

There are **8 divisors** in total. Therefore, the correct answer is **eight**.

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Would you like further details or have any questions?

Here are five questions to expand on this concept:

1. What is the prime factorization of other numbers like 60 or 100?
2. How do you find the number of divisors from the prime factorization?
3. How many divisors does a perfect square like 36 have?
4. What is the difference between prime and composite divisors?
5. How are divisors related to the greatest common divisor (GCD)?

**Tip**: To quickly find the number of divisors, use the exponents in the prime factorization and apply the divisor formula.

How many whole numbers can divide 30 exactly?

Explore how to find the divisors of 30 through prime factorization. Understand the mathematical concepts of divisibility and number theory. Suitable for students in Grades 5-7, this step-by-step guide helps you calculate the divisors of any number using the Divisor Theorem.

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