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5 Prime Time

5.1 INTRODUCTION Learning Outcomes

Numbers are all around us! Some numbers are special By the end of this chapter, students will be able to:
because they follow unique rules, making them stand out. • Understand and define prime and composite
For instance, did you know that the number 7 cannot be numbers using factors and multiples.
divided evenly by any other number except 1 and itself? • Explain the role of prime numbers in factorisation.
But wait, what about the number 6? It can be divided • Use divisibility rules to check if a number is prime
or composite.
evenly by 1, 2, 3, and 6. • Perform prime factorisation of numbers.

What are these two different types of numbers? • Solve real-life problems using concepts of prime
Have you ever wondered why some numbers numbers and prime factorisation.
seem to divide so neatly into others while others don’t?
Have you ever tried to share candies equally among your friends or wondered how fast you can skip
count by 5s or 10s?
We will find the answer to all these questions through this chapter.

5.2 FACTORS AND MULTIPLES

We are already familiar with dividing a whole number by a smaller whole number. Let’s recall the division
algorithm from Chapter 3:

If the whole number ‘a’ is divided by another non-zero smaller whole number ‘b’, then there exist unique
whole numbers ‘q’ and ‘r’, such that ‘a’ can be written as

a = (b × q) + r, 0 ≤ r < b,

where ‘q’ is called the quotient, ‘r’ is the remainder, ‘a’ is the dividend, and ‘b’ is the divisor.

For example, if 33 is divided by 7, we get 4 as the quotient, 5 as the remainder, and the division algorithm
can be written as 33 = 7 × 4 + 5.
Wait! Can you tell what happens when 33 is divided by 3 instead of 7?
Yes, you are right. The remainder is ‘0’ now, and we have 33 = 3 × 11.

So, there are situations when dividing a whole number by another leaves the remainder 0, and the above-
mentioned division algorithm reduces to:

a = b × q ( r = 0)

Then, ‘b’ and ‘q’ both are called Factors or Divisors of ‘a’, and ‘a’ is known as a Multiple of ‘b’ and ‘q’ both.

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