Be My Multiple, I'll Be Your Factor - Class 5 Maths Chapter 6

Chapter 6 of Class 5 Maths, 'Be My Multiple, I'll Be Your Factor', introduces two very important number ideas — factors and multiples. Think of factors as the small numbers that divide a bigger number exactly, and multiples as the numbers you get by multiplying a number again and again. For example, 3 is a factor of 12, and 12 is a multiple of 3 — this is exactly the friendly relationship the chapter title talks about. In this page, you will learn how to find all factors of a number, how to list multiples, understand even and odd numbers, learn about prime and composite numbers, and discover simple tricks like divisibility rules. These ideas form the foundation for later topics like HCF, LCM, and fractions in higher classes, so mastering them now with clear examples and plenty of practice will make your future maths much easier and more confident.

Understanding Factors and Multiples

A factor of a number is a number that divides it completely, leaving no remainder. For example, factors of 12 are 1, 2, 3, 4, 6 and 12 because each of these divides 12 exactly.

A multiple of a number is what you get when you multiply that number by 1, 2, 3, 4, and so on. Multiples of 4 are 4, 8, 12, 16, 20... and they go on forever — there is no last multiple!

The special connection: if 4 is a factor of 12, then 12 is automatically a multiple of 4. That is why the chapter is playfully named 'Be My Multiple, I'll Be Your Factor' — the two ideas are like partners, always found together, just viewed from opposite directions.

Key Terms You Must Know

Factor
A number that divides another number exactly without leaving a remainder. Every number has at least two factors: 1 and itself.
Multiple
The result of multiplying a number by 1, 2, 3, 4... Multiples of any number are infinite.
Prime number
A number greater than 1 that has exactly two factors: 1 and itself. Example: 2, 3, 5, 7, 11.
Composite number
A number greater than 1 that has more than two factors. Example: 4, 6, 8, 9, 10.
Even number
A number that is a multiple of 2, ending in 0, 2, 4, 6 or 8.
Odd number
A number that is not a multiple of 2, ending in 1, 3, 5, 7 or 9.

Worked Examples - Step by Step

  • Find all factors of 18.
    Step 1: Start dividing 18 by 1, 2, 3... and check which divide exactly.
    18 ÷ 1 = 18 (factor pair 1,18)
    18 ÷ 2 = 9 (factor pair 2,9)
    18 ÷ 3 = 6 (factor pair 3,6)
    18 ÷ 4 = not exact
    18 ÷ 5 = not exact
    Step 2: Since 6 already appeared, we stop (we have crossed the middle point).
    Final answer: Factors of 18 = 1, 2, 3, 6, 9, 18.

  • Write the first 5 multiples of 7.
    Step 1: Multiply 7 by 1, 2, 3, 4, 5.
    7×1=7, 7×2=14, 7×3=21, 7×4=28, 7×5=35
    Final answer: 7, 14, 21, 28, 35.

  • Check whether 6 is a factor of 42.
    Step 1: Divide 42 by 6.
    42 ÷ 6 = 7, remainder 0.
    Step 2: Since remainder is 0, 6 divides 42 exactly.
    Final answer: Yes, 6 is a factor of 42, and 42 is a multiple of 6.

  • Is 29 a prime or composite number?
    Step 1: Check divisibility by small numbers: 2 (no, 29 is odd), 3 (2+9=11, not divisible by 3), 5 (does not end in 0 or 5), and we stop since next number 6×6=36 is greater than 29.
    Step 2: No factor found other than 1 and 29.
    Final answer: 29 is a prime number.

Quick Divisibility Rules to Find Factors Fast

  1. Rule for 2 — A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8. Example: 348 ends in 8, so 2 is a factor of 348.
  2. Rule for 3 — Add all digits of the number. If the sum is divisible by 3, the number is too. Example: 231 → 2+3+1=6, and 6 is divisible by 3, so 3 is a factor of 231.
  3. Rule for 5 — A number is divisible by 5 if it ends in 0 or 5. Example: 175 ends in 5, so 5 is a factor of 175.
  4. Rule for 10 — A number is divisible by 10 if it ends in 0. Example: 560 ends in 0, so 10 is a factor of 560.
  5. Rule for 9 — Add all digits. If the sum is divisible by 9, the number is too. Example: 549 → 5+4+9=18, and 18 is divisible by 9, so 9 is a factor of 549.

Common Mistakes and Exam Tips

  • Do not confuse factors with multiples — factors are always less than or equal to the number, while multiples are always greater than or equal to the number.
  • Remember 1 is a factor of every number, but 1 is neither prime nor composite.
  • When listing multiples, students often stop too early — always write at least the first 5-10 multiples as asked.
  • While finding factors, check divisibility only up to the square root of the number (you can stop once pairs start repeating) to save time.
  • 2 is the only even prime number — a very common exam trick question.

Board Exam Tip

In CBSE Class 5 worksheets, questions often ask you to find common factors or common multiples of two numbers. Always list the factors/multiples of each number separately first, then circle the numbers that appear in both lists. This simple method avoids confusion and helps you correctly identify the Highest Common Factor (HCF) or Lowest Common Multiple (LCM) basics, which you will study formally in later classes.

Practice Questions with Solutions

  • Q: Find all the factors of 24.
    A: Step 1: Check numbers from 1 upward: 24÷1=24, 24÷2=12, 24÷3=8, 24÷4=6, 24÷5=not exact.
    Step 2: We reached 4 and 6 which are close together, so we stop.
    Final answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

  • Q: List the first 6 multiples of 9.
    A: Step 1: Multiply 9 by 1,2,3,4,5,6.
    9×1=9, 9×2=18, 9×3=27, 9×4=36, 9×5=45, 9×6=54.
    Final answer: 9, 18, 27, 36, 45, 54.

  • Q: Find the common factors of 12 and 18.
    A: Step 1: Factors of 12 = 1, 2, 3, 4, 6, 12.
    Step 2: Factors of 18 = 1, 2, 3, 6, 9, 18.
    Step 3: Compare both lists and pick common numbers: 1, 2, 3, 6.
    Final answer: Common factors of 12 and 18 are 1, 2, 3, 6.

  • Q: Is 51 a prime number or a composite number?
    A: Step 1: Check divisibility: 51 is odd so not divisible by 2. Add digits 5+1=6, which is divisible by 3, so 51÷3=17 exactly.
    Step 2: Since 51 has factors 1, 3, 17, 51 (more than two factors).
    Final answer: 51 is a composite number.

  • Q: Find the first common multiple (other than 0) of 4 and 6.
    A: Step 1: Multiples of 4 = 4, 8, 12, 16, 20, 24...
    Step 2: Multiples of 6 = 6, 12, 18, 24, 30...
    Step 3: The smallest number appearing in both lists is 12.
    Final answer: The lowest common multiple of 4 and 6 is 12.

Frequently Asked Questions

What is the main difference between a factor and a multiple?

A factor divides a number exactly and is always smaller than or equal to that number, while a multiple is obtained by multiplying a number and is always greater than or equal to it. For example, 4 is a factor of 12, but 12 is a multiple of 4.

Is 1 a prime number?

No, 1 is neither prime nor composite because a prime number must have exactly two different factors, but 1 has only one factor, which is itself. This is a common exam trap, so remember it carefully.

How many multiples does a number have?

Every number has infinite multiples because you can keep multiplying it by 1, 2, 3, 4 and so on without any end. However, the number of factors of a given number is always limited.

What is the smallest prime number and is it even?

The smallest prime number is 2, and it is also the only even prime number. All other even numbers greater than 2 are composite because they are divisible by 2 and themselves.

How do divisibility rules help in finding factors?

Divisibility rules let you quickly check whether a small number like 2, 3, 5, 9 or 10 divides a larger number without doing long division. This saves time when listing all factors of a number in exams.