Class 5 — Mathematics
Factors, Multiples, HCF & LCM
Class 5
- ✓By the end of this lesson students will be able to identify factors and multiples of given numbers.
- ✓By the end of this lesson students will be able to distinguish between prime and composite numbers.
- ✓By the end of this lesson students will be able to find the Highest Common Factor (HCF) of two numbers.
- ✓By the end of this lesson students will be able to find the Least Common Multiple (LCM) of two numbers.
Key concepts
A factor of a number is a number that divides it exactly, leaving no remainder. For example, to find the factors of 12, we find all numbers that divide 12 without leaving a remainder. These are 1, 2, 3, 4, 6, and 12. Every number has 1 and itself as factors. Factors are always less than or equal to the number.
A multiple of a number is the product of that number and any counting number (1, 2, 3, 4, ...). For example, to find the multiples of 5, we multiply 5 by 1, 2, 3, and so on. The multiples of 5 are 5, 10, 15, 20, 25, ... Multiples of a number are always greater than or equal to the number. Multiples of a number are infinite.
A prime number is a number that has exactly two factors: 1 and the number itself. For example, 2 is a prime number because its only factors are 1 and 2. Other examples include 3 (factors: 1, 3), 5 (factors: 1, 5), 7 (factors: 1, 7), etc. The number 1 is neither prime nor composite.
A composite number is a number that has more than two factors. For example, 4 is a composite number because its factors are 1, 2, and 4 (more than two factors). Other examples include 6 (factors: 1, 2, 3, 6), 8 (factors: 1, 2, 4, 8), 9 (factors: 1, 3, 9), etc.
The Highest Common Factor (HCF) of two or more numbers is the largest factor that is common to all of them. To find the HCF, we list all the factors of each number, identify the factors that are common to all numbers, and then select the largest among these common factors.
The Least Common Multiple (LCM) of two or more numbers is the smallest non-zero multiple that is common to all of them. To find the LCM, we list the multiples of each number until we find the first (smallest) multiple that appears in all the lists.
Key facts to remember
- 11 is a factor of every number.
- 2Every number is a factor of itself.
- 3Every number is a multiple of itself.
- 4Multiples of a number are infinite.
- 5Factors of a number are finite.
- 6Prime numbers have exactly two factors: 1 and the number itself.
- 7Composite numbers have more than two factors.
- 8The number 1 is neither prime nor composite.
Worked examples
Example 1
Find all factors of 28. Is 28 a prime or composite number?
Answer
The factors of 28 are 1, 2, 4, 7, 14, 28. 28 is a composite number.
Remember, a prime number has exactly two factors: 1 and itself. A composite number has more than two factors.
Example 2
Find the HCF of 12 and 18.
Answer
The HCF of 12 and 18 is 6.
Always list all factors carefully to avoid missing any common factors.
Example 3
Find the LCM of 4 and 6.
Answer
The LCM of 4 and 6 is 12.
Continue listing multiples until you find the first common one. The LCM is always a non-zero number.
Common mistakes
- ✗Confusing factors and multiples (e.g., listing multiples when asked for factors).
- ✗Incorrectly identifying 1 as a prime number.
- ✗Missing some factors when listing them for a number.
- ✗Stopping listing multiples too early and missing the actual LCM.
- ✗Confusing HCF with LCM (e.g., finding the smallest common factor instead of the largest, or vice-versa).
Exam tips
- ★Read the question carefully to understand whether you need to find factors, multiples, HCF, or LCM.
- ★Show all your working steps clearly, especially when listing factors or multiples.
- ★Double-check your lists of factors and multiples to ensure accuracy.
- ★Practice finding factors, multiples, HCF, and LCM for various numbers regularly.
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