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Unit 1: Prime and Composite
Numbers factors and
Multiples
Course no. DTE-432
Subject: Teaching of Mathematics
Compiled by: Naveen Siddiqui

What are prime numbers?
 Prime numbers are positive integers (whole
numbers) that have only two factors.
 This means that you cannot divide a prime number by
any number.
 A number that is not prime is called a composite
number.
 There are 25 prime numbers between 1 and 100.
These are:
 2,3,5,7,11,13,17,19,23,29, 31,37,41,43,47,53,59,61,67,71,7
3,79,83,89,and 97.

Link to show Sieve of Erathothenes for
prime no.
 https://youtu.be/V08g_lkKj6Q?
si=vF0vkBC3zd5OBQ0X

unit 1 prime and composite factors and multiples.pptx

 To determine whether the number is prime,
check whether it has any factors other than itself
and 1, either manually or by using a number
trick. If the number has a factor that is not itself
or 1, it is not prime.

To Check Prime no.
 Is 53 a prime number?
Step 1: Use the number tricks to see
whether 2,3 or 5 is a factor.
 The last digit is not a 2,4,6,8,and 0 so it is not a
multiple of 2.
 Adding the digits together we have 5+3=8 and so it
is not a multiple of 3.
 The last digit is not a 5 or a 0 and so it is not a
multiple of 5.

Step 2: If they are not factors, test for divisibility by other
prime numbers, starting with 7.
As 53÷7=7.57142857 is not a factor of 53.
The next prime number is 11, which is greater than 7.3 so
there are no more integers that we need to try.
Step 3: State your conclusion with a reason.
53 is a prime number as it only has two factors, 1and 53.

Task
 Is 223 a prime number or 2073 a prime no?

Home Task
One of the following numbers is prime. Identify
the prime number.
4 25 9 61 259
1. Use the number tricks to see whether 2,3 or 5 is a factor.
2. If they are not factors, test for divisibility by other prime
numbers, starting with 7.
3. State your conclusion with a reason.

Difference between
Factors and Multiples.

What Are Factors and Multiples?
 Factors and multiples are two interrelated
concepts in mathematics. If A×B=C, then A and
B are factors of C, whereas C is a multiple of
both A and B

What Are Factors?
 A factor is a number that divides the given number
exactly, without any remainder. When a number n is
divisible by b, we can say that b is a factor of n.
 For example, the factors of 16 are 1, 2, 4, 8, and 16,
because these numbers divide 16 exactly, without leaving
any remainder.

Properties of Factors
 1 is the smallest factor of any number.
 The number itself is the greatest factor of any
number.
 A factor of a number is always less than or equal
to the number.
 Factors of a number are finite.
 0 cannot be a factor of any number.

What Are Multiples?
 A multiple of a number is the number obtained when the
given number is multiplied with an integer.
 A multiple is a result of multiplying a number by an
integer. Note that, when we study multiples of any
number, we generally talk about positive multiples only
(excluding 0 and negative multiples). Thus, we can say
that a multiple is the number obtained by multiplying a
given number by a positive integer.
 For example, the multiples of 5 are 5, 10, 15, 20,…, and so
on, because these numbers can be obtained by
multiplying 5 with the whole numbers 1, 2, 3, 4,…, and so
on.

Properties of Multiples
 Infinitely many multiples of any number.
 A multiple is always greater than or equal to the
given number.
 Every number is a multiple of 1.
 0 is considered a multiple of every number.

Difference Between Factors and Multiples
Factors Multiples
Factors are numbers that divide the
given number without leaving a
remainder.
Multiples are the numbers obtained
as a product of a given number and
integers.
A factor of a number is less than or
equal to itself.
Multiples are always greater than
or equal to the given number.
Factors are finite in number and
include 1 and the number itself.
There are an infinite number of
multiples for a given number.
1 is the smallest factor of any
number.
Every number is a multiple of 1.
0 cannot be a factor of any number. 0 is a multiple of every number.
Example: Factors of 8 are 1, 2, 4, 8.
Example: Multiples of 8 are 8, 16,
24,…

Rectangle lesson for fraction
 Draw the rectangles with areas of 10 on the
paper.

How can we find factors?
 To find the factors of a given number, divide the
number by each integer between 1 and the
number itself. The integers that give us a
remainder of 0 are factors of the number.
 For example, to find the factors of 6, divide 6 by
numbers 1 to 6.
 The factors of 6
are 1, 2, 3, and 6.
6/1 Remainder =0
6/2 Remainder =0
6/3 Remainder =0
6/4 Remainder =1.5
6/5 Remainder =1
6/6 Remainder =0

How to find multiples
 To find the multiples of a given number, multiply
the number by each positive integer.
For example, to find the multiples of 5, you would
multiply 5 by 1, 2, 3, 4, and so on.
 Multiples of 5=5,10,15,20,25, …
 Multiples of 9=9,18,27,36,45, …

Task
 Find the factors of 30.

 Solution:
 The factors of 30 are the integers that divide 30
without leaving any remainder.
 30÷1=30 and remainder=0
 30÷10 =3 and remainder = 0
 Thus, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and
30.

Task
 Find the multiples of 7 that are less than or
equal to 56.

 Solution:
 We can write the multiples of 7 as,
 7×1=7
 7×2=14
 7×3=21
 7×4=28
 7×5=35
 7×6=42
 7×7=49
 7×8=56
 Hence, the multiples of 7 that are less than or
equal to 56 are 7, 14, 21, 28, 35, 42, 49, and 56.

Home Task
Create a T-chart on the board.
 On one side, write down what they did not learn
about these topic when they were children
 On the other side, write what they now
understand about prime and composite no and
factors and multiples.

Division of Whole no.
And
Modelling Division with
Partitive Method and
Measurement Method

Two ways of thinking of division practice
problems
Partitive Measurement
In a partitive division, you know how
many groups to split it into, and you
need to figure out how many in each
group.
Example: 15 ÷ 3
 take out 15 counters
 do something to show where the 3
groups will be
 give counters one at a time (or two
at a time) to each group until the
counters are gone, and the groups
all have the same amount
 count the amount in 1 group.
In a measurement division problem
,you know how many should go in
each group, and you have to figure
out how many groups there will be.
Example 15 ÷ 3 take out 15 counters
 make a set of 3 from the 15
counters, and then continue
making sets of 3 until all of the
counters are used
 count how many sets of 3 you
have made.

Link to be shown
https://youtu.be/65ZHYUhSxyc?
si=xG3YTzmzlx7RZh9l

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unit 1 prime and composite factors and multiples.pptx

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