1. Exploring Number Relationships
1. Exploring Number Relationships
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Recall multiplication and division facts
Recognize the factors of a given number.
Recall and identify the multiples of a given number.
Recall prime and composite numbers
Multiplication and Division Fact Families
They are related multiplication and division equations that use the same three numbers to create four different equations - 2 multiplication and 2 division equations.
a. What is a multiplication fact?
A multiplication fact is the product of two specific numbers. The order in which the numbers are presented does not change the product1.
For example, 2×3=6 and 3×2=6.
b. What is a Division Fact?
Division facts are number phrases that relate to knowing the times tables.
For example: 20 ÷ 5 = 4 and 20 ÷ 4 = 5
For example: The fact family for 2, 6 and 12 is a set of four multiplication and division facts.
Two are multiplication facts, whereas the other two are division facts.
Multiplication facts: 2 x 6 = 12; 6 x 2 =12
Division facts: 12 ÷ 2 = 6; 12 ÷ 6 =2
Fig 1.1: Practice Multiplication And Divison Facts 2
Factors are numbers that divide the given number without leaving a remainder. A factor of a number is less than or equal to itself.3
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.
If B is a multiple of A, then A is a factor of B.
Watch the video to learn more about Factors.
Vid 1.1 Learning Factors
Grassy jumps 3 steps at a time starting from 1. Cricky jumps 4 steps at a time starting from 1.
You will find that grassy jumps on 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30.
These are called the multiples of 3.
The numbers that cricky will jump on will be 4, 8, 12, 16, 20, 24 and 28..
These are the multiples of 4.
When two or more numbers are multiplied, the product is called the multiple of those numbers. Multiples are always greater than or equal to the given number.
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.
If B is a multiple of A, then A is a factor of B.
0 is considered a multiple of every number.
Watch the video to learn more about Multiples
Vid 1.2 Multiples
Prime Numbers: A prime number is a number which has exactly two factors i.e. ‘1’ and the number itself.
Example:
3 is a prime number because 3 can be divided by only two numbers i.e. 1 and 3 itself.
In the same way, 2, 5, 7, 11, 13, 17 are prime numbers.
Composite Numbers: A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one other number.4
Important: 1 is neither a prime number nor a composite number.
Example:
3 is a prime number because 3 can be divided by only two numbers i.e. 1 and 3 itself.
Some more examples of composite numbers are:
Summary :-
1. A multiplication fact is the product of two specific numbers.
2. Division facts are number phrases that relate to knowing the times tables.
3. Factors are numbers that divide the given number without leaving a remainder.
4. When two or more numbers are multiplied, the product is called the multiple of those numbers.
5. A prime number is a number which has exactly two factors i.e. ‘1’ and the number itself.
6. A composite number has more than two factors.
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