Introduction
Factors, Multiples, Prime, and Composite Numbers is an important Grade 4 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with factors, multiples, prime, and composite numbers.
What Is Factors, Multiples, Prime, and Composite Numbers?
Factors, Multiples, Prime, and Composite Numbers means using place value, operations, and equations to reason accurately with numbers.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Factors, Multiples, Prime, and Composite Numbers
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Complete the factor pair table for \(20\): What goes in the ?
- A. \(8\)
- B. \(15\)
- C. \(12\)
- D. \(10\)
Why it works: We need a number that pairs with \(2\) to make \(20\). Ask yourself: \(2 \times \,? = 20\). Since \(2 \times 10 = 20\), the missing factor is \(\mathbf{10}\).
Answer: \(10\)
Visual Model 2
Question: The factors of \(18\) are shown in the table. Which number is missing?
| Factor Pair |
|---|
| \(1 \times 18 = 18\) |
| \(2 \times 9 = 18\) |
| \(3 \times ? = 18\) |
- A. \(5\)
- B. \(9\)
- C. \(7\)
- D. \(6\)
Why it works: We need a number that pairs with \(3\) to make \(18\). Ask: \(3 \times \,? = 18\). Since \(3 \times 6 = 18\), the missing factor is \(\mathbf{6}\).
Answer: \(6\)
Worked Examples
Example 1
Question: Look at the factor pairs of \(36\) shown in a rainbow diagram. How many factor pairs does \(36\) have?
- A. \(4\)
- B. \(7\)
- C. \(6\)
- D. \(5\)
- Walk the rainbow!
- The pairs that multiply to \(36\) are \((1,36), (2,18), (3,12), (4,9), (6,6)\).
- Notice \((6,6)\) is special---it's a "square" pair where both factors are the same.
- Count: \(\mathbf{5}\) pairs.
Answer: \(5\)
Example 2
Question: Count the multiples of \(8\) between \(1\) and \(60\) using the table: How many multiples of \(8\) are there up to \(60\)?
| \(8\) | \(16\) | \(24\) | \(32\) |
|---|---|---|---|
| \(40\) | \(48\) | \(56\) | next is \(64\) |
- A. \(6\)
- B. \(9\)
- C. \(8\)
- D. \(7\)
- Read across the table: \(8, 16, 24, 32, 40, 48, 56\).
- The next one (\(64\)) is over \(60\), so we stop.
- Count: \(\mathbf{7}\) multiples of \(8\) up to \(60\).
Answer: \(7\)
Example 3
Question: Complete the table of factor pairs for \(42\):
| First Factor | Second Factor |
|---|---|
| \(1\) | \(42\) |
| \(2\) | \(21\) |
| \(3\) | ? |
| \(6\) | \(7\) |
- A. \(12\)
- B. \(39\)
- C. \(18\)
- D. \(14\)
- We need a number that pairs with \(3\) to make \(42\).
- Ask: \(3 \times \,? = 42\).
- Since \(3 \times 14 = 42\), the missing factor is \(\mathbf{14}\).
Answer: \(14\)
Real-World Word Problems
Problem 1
Question: Which of the following is a prime number?
- A. \(9\)
- B. \(15\)
- C. \(17\)
- D. \(21\)
Why it works: A prime number has exactly two factors: \(1\) and itself. Try dividing \(17\): it doesn't divide evenly by \(2\), \(3\), \(4\), or \(5\), so its only factors are \(1\) and \(17\)---prime! The others are composite: \(9 = 3 \times 3\); \(15 = 3 \times 5\); \(21 = 3 \times 7\).
Answer: \(17\)
Problem 2
Question: What are all the factors of \(12\)?
- A. \(1, 3, 5, 7, 12\)
- B. \(1, 2, 4, 6, 12\)
- C. \(2, 3, 4, 6, 12\)
- D. \(1, 2, 3, 4, 6, 12\)
Why it works: Factors are numbers that divide evenly with no remainder. Walk through the factor pairs: \(1 \times 12\), \(2 \times 6\), \(3 \times 4\). Listing every factor: \(1, 2, 3, 4, 6, 12\). Tip: pair them up as you go---it makes sure you don't miss any!
Answer: \(1, 2, 3, 4, 6, 12\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Is \(11\) prime or composite?
- A. Neither prime nor composite
- B. Composite
- C. Both prime and composite
- D. Prime
Question 2
Which list shows consecutive multiples of \(5\) starting at \(5\)?
- A. \(5, 10, 15, 20, 25\)
- B. \(5, 15, 20, 35, 40\)
- C. \(5, 10, 15, 20, 30\)
- D. \(10, 20, 30, 40, 50\)
Question 3
Which pair shows factors of \(24\)?
- A. \(3\) and \(8\)
- B. \(4\) and \(5\)
- C. \(5\) and \(5\)
- D. \(2\) and \(10\)
Question 4
Is \(25\) prime or composite?
- A. Prime
- B. Both
- C. Neither
- D. Composite
Question 5
Which number is divisible by \(2\)?
- A. \(47\)
- B. \(71\)
- C. \(63\)
- D. \(52\)
Question 6
How many multiples of \(10\) are there from \(1\) to \(50\)?
- A. \(3\)
- B. \(4\)
- C. \(5\)
- D. \(6\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: Prime
Try dividing \(11\) by \(2, 3, 4, 5\)---none of them divide evenly. So \(11\)'s only factors are \(1\) and itself. Exactly two factors = prime.
Question 2
Answer: \(5, 10, 15, 20, 25\)
Multiples of \(5\) are what you get when you skip-count by \(5\): \(5, 10, 15, 20, 25, \ldots\) Choice A counts in order with no skips. Choice B jumps \(10 \to 20 \to 35\) (gaps); choice C jumps over \(25\); choice D starts at \(10\) instead of \(5\).
Question 3
Answer: \(3\) and \(8\)
A factor pair has to multiply to give \(24\). Test each: \(3 \times 8 = 24\) \checkmark; \(4 \times 5 = 20\); \(5 \times 5 = 25\); \(2 \times 10 = 20\). Only choice A multiplies to exactly \(24\).
Question 4
Answer: Composite
Look for any factor besides \(1\) and itself. \(25 = 5 \times 5\), so \(5\) is a factor too. That gives factors \(1, 5, 25\)---more than two---so \(25\) is composite.
Question 5
Answer: \(52\)
Divisibility rule for \(2\): the last digit must be even (\(0, 2, 4, 6, 8\)). \(52\) ends in \(2\)---even! So \(52 \div 2 = 26\). The others (\(47, 63, 71\)) end in odd digits, so they don't divide evenly by \(2\).
Question 6
Answer: \(5\)
Skip-count by \(10\) from \(10\) up to \(50\): \(10, 20, 30, 40, 50\). That's \(\mathbf{5}\) multiples in the range. Quick way: \(50 \div 10 = 5\).
Connection to Standards
This lesson supports Grade 4 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Factors, Multiples, Prime, and Composite Numbers becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
