Mathematics
Chapter 1.
Square numbers
Numbers that form square patterns are called square numbers (e.g. 1, 4, 9,
16, 25, 36)
Multiples of whole numbers
Multiples of a whole number are numbers that can be divided by the certain
whole number. For example, 5 × 7 = 35, which means that 35 is a
multiple of 5 and it is also a multiple of 7
Multiples of 5 are: 5 10 15 20 25 30 35...
Multiples of 7 are: 7 14 21 28 35 42...
Factors of whole numbers
A factor of whole number is any whole number that divides into it
exactly.
Factor facts
1 is always a factor and so the number itself
When you found one factor, there is always another factor that
goes with it- unless the factor is multiplied by itself to give the
number – and they are usually called factor pairs.
Lowest common multiple
The lowest common multiple (LCM) of two numbers is smallest
number that appears in the multiplication tables of both numbers.
For example, the LCM of 3 and 5 is 15, the LCM of 2 and 7 is 14.
, Highest common factor
The highest common factor (HCF) of two numbers is the biggest number
that divides exactly into both of them
For example, the HCF of 24 and 18 is 6, the HCF of 45and 36 is 9 and
HCF of 15 and 22 is 1.
Prime numbers
Numbers that have only two factors: itself and 1 are examples of prime
factors.
Note: 1 is not a prime number, since it has only one factor-itself.
The prime numbers up to 50 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
Prime factorization
Every whole number that is not a prime can be written as the product of
prime factors. For example:
35= 5 × 7
40= 2 × 2 × 2 × 5
5 and 7 are the prime factors of 35
2 and 5 are the prime factors of 40
Indices can be used to write the product more easily. For example:
40= 2^3 × 5 -The small 3 is an index-
Writing a number in this way is called prime factorization.
Prime factorization can also be used to find the LCM or the HCF
of two or more numbers.
Chapter 1.
Square numbers
Numbers that form square patterns are called square numbers (e.g. 1, 4, 9,
16, 25, 36)
Multiples of whole numbers
Multiples of a whole number are numbers that can be divided by the certain
whole number. For example, 5 × 7 = 35, which means that 35 is a
multiple of 5 and it is also a multiple of 7
Multiples of 5 are: 5 10 15 20 25 30 35...
Multiples of 7 are: 7 14 21 28 35 42...
Factors of whole numbers
A factor of whole number is any whole number that divides into it
exactly.
Factor facts
1 is always a factor and so the number itself
When you found one factor, there is always another factor that
goes with it- unless the factor is multiplied by itself to give the
number – and they are usually called factor pairs.
Lowest common multiple
The lowest common multiple (LCM) of two numbers is smallest
number that appears in the multiplication tables of both numbers.
For example, the LCM of 3 and 5 is 15, the LCM of 2 and 7 is 14.
, Highest common factor
The highest common factor (HCF) of two numbers is the biggest number
that divides exactly into both of them
For example, the HCF of 24 and 18 is 6, the HCF of 45and 36 is 9 and
HCF of 15 and 22 is 1.
Prime numbers
Numbers that have only two factors: itself and 1 are examples of prime
factors.
Note: 1 is not a prime number, since it has only one factor-itself.
The prime numbers up to 50 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
Prime factorization
Every whole number that is not a prime can be written as the product of
prime factors. For example:
35= 5 × 7
40= 2 × 2 × 2 × 5
5 and 7 are the prime factors of 35
2 and 5 are the prime factors of 40
Indices can be used to write the product more easily. For example:
40= 2^3 × 5 -The small 3 is an index-
Writing a number in this way is called prime factorization.
Prime factorization can also be used to find the LCM or the HCF
of two or more numbers.
