Operations & Algebraic Thinking
Exploring Factors, Multiples, Prime, Composite, and Multiplicative Comparisons
Grade 4
- ✓By the end of this lesson students will be able to identify factors and multiples of whole numbers within 100.
- ✓By the end of this lesson students will be able to distinguish between prime and composite numbers within 100.
- ✓By the end of this lesson students will be able to interpret and solve word problems involving multiplicative comparisons.
- ✓By the end of this lesson students will be able to recognize and extend number patterns related to factors and multiples.
Key concepts
A factor of a whole number is a whole number that divides it exactly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers can divide 12 without a remainder.
A multiple of a whole number is the product of that number and any other whole number (except zero). Multiples are like skip-counting. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. For example, 7 is a prime number because its only factors are 1 and 7.
A composite number is a whole number greater than 1 that has more than two factors. For example, 10 is a composite number because its factors are 1, 2, 5, and 10 (more than two factors).
Multiplicative comparison is a way to compare two quantities by stating that one quantity is a certain number of times as large as the other. It often uses phrases like 'times as many' or 'times as much'. For example, 'John has 3 times as many apples as Mary' is a multiplicative comparison.
Key facts to remember
- 1The number 1 is neither prime nor composite.
- 2Every whole number greater than 1 has at least two factors: 1 and itself.
- 3The only even prime number is 2.
- 4Multiples of a number are infinite; they go on forever.
- 5Factors of a number are always less than or equal to the number itself.
- 6All prime numbers (except 2) are odd, but not all odd numbers are prime (e.g., 9 is odd but composite).
- 7Multiplicative comparison problems can be solved using multiplication or division.
Worked examples
Example 1
Find all factors of 18. Is 18 a prime or composite number? List the first 5 multiples of 6.
Answer
Factors of 18: 1, 2, 3, 6, 9, 18. 18 is a composite number. First 5 multiples of 6: 6, 12, 18, 24, 30.
Remember to check factors systematically, starting from 1, to make sure you don't miss any.
Example 2
Emily has 7 marbles. Her friend, David, has 4 times as many marbles as Emily. How many marbles does David have?
Answer
David has 28 marbles.
Example 3
A blue rope is 36 feet long. A red rope is 3 times shorter than the blue rope. How long is the red rope?
Answer
The red rope is 12 feet long.
The phrase 'times shorter' means you should divide, not subtract.
Common mistakes
- ✗Confusing factors with multiples (e.g., listing multiples when asked for factors).
- ✗Incorrectly identifying 1 as a prime number.
- ✗Forgetting to list all factors of a number, especially the number itself.
- ✗Misinterpreting 'times shorter' or 'times less' as subtraction instead of division in multiplicative comparison problems.
- ✗Assuming all odd numbers are prime numbers.
Exam tips
- ★When finding factors, always start with 1 and work your way up systematically to ensure you find all factor pairs.
- ★For prime/composite questions, list all factors to be sure. If there are only two factors (1 and itself), it's prime. If more, it's composite.
- ★For multiplicative comparison word problems, draw a bar model or a picture to help visualize the relationship between the quantities.
- ★Read word problems carefully to identify keywords like 'times as many,' 'times as much,' or 'times shorter' to determine whether to multiply or divide.
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