HCF, LCM, Prime Numbers, and Factors in Mathematics
Highest Common Factor and Lowest
Common Multiple
HCF and LCM
Prime Numbers and Prime Factors
To
study
the
highest
common
factor
and
lowest
common
multiple
of
a
pair
of
numbers
we
first
have
to
understand
some
of
the
basics
.
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*
*
Although
the
number
1
fits
the
definition
,
it
is
NOT
regarded
as
a
prime
number
.
The
first
prime
number
(
and
the
ONLY
even
prime
number
)
is
2
W
h
a
t
i
s
a
P
R
I
M
E
F
A
C
T
O
R
?
A
n
u
m
b
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w
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.
To evaluate the HCF and LCM of a pair of numbers means that we have to have a GOOD
understanding of prime numbers and prime factors. Before we look at HCF and LCM we will
look at these more closely
Factors
A number is a factor of another number if it divides wholly into the other number leaving NO
remainder or fractional part.
12
1 2 3 4 5 6 7
8 9 10 11 12
Prime Numbers
This table contains all of the prime
numbers between 1 and 200.
You will find it useful to try to memorise
at least the primes up to 100.
Prime Factors
To factorise a number using prime factors is done by dividing the number (and the result of
that division) by the lowest prime, moving to the next suitable prime when the division stops.
Sounds weird?
Lets take a look at an example, this will clear up the confusion.
36
9 doesn’t divide by 2 so we move to the
next prime which is 3.
We are left with 3, we stop here and list our
prime factors.
Prime Factors
We usually lay out the numbers as a sort of “tree” so you will hear the expression “prime factor
tree” in your maths work.
Here are a couple of “prime factor trees”
Hot Spot 1a
Q1. Produce a prime factor tree for the number 56
56
2
56
28
2
14
2
7
Hot Spot 1b
Q2. Produce a prime factor tree for the number 180
2
180
90
2
45
3
15
3
5
Lowest Common Multiple
The LCM is the LOWEST number that is a multiple of two numbers.
Example - Find the LCM of the numbers 6 and 8
Common factors are counted only once so the LCM of 6 and 8 is 24
Lowest Common Multiple
The LCM is the LOWEST number that is a multiple of two numbers.
Example - Find the LCM of the numbers 8 and 12
Common factors are counted only once so the LCM of 8 and 12 is 24
Hot Spot 2
Find the lowest common multiple of each of the following number pairs:
Highest Common Factor
The HCF is a little easier to work out. We simply write out the factors of each of the pair and
calculate the largest common factor in each list by expanding the common factors:
Example: Find the HCF of 26 and 34
Highest Common Factor
The HCF is a little easier to work out. We simply write out the factors of each of the pair and
calculate the largest common factor in each list by expanding the common factors:
Example: Find the HCF of 64 and 244
Highest Common Factor
The HCF is a little easier to work out. We simply write out the factors of each of the pair and
calculate the largest common factor in each list by expanding the common factors:
Example: Find the HCF of 56 and 425
There are NO COMMON
FACTORS between 56 and
425.
In these cases the HCF is 1
as 1 is a factor of ANY
number.
Hot Spot 3
Find the highest common factor of each of the following number pairs:
Delve into the concepts of Highest Common Factor (HCF), Lowest Common Multiple (LCM), Prime Numbers, and Factors. Learn how to identify prime factors and how they relate to calculating the HCF and LCM of numbers. Explore prime factorization through visual tools like factor trees to enhance your understanding.
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Presentation Transcript
Highest Common Factor and Lowest Common Multiple HCF and LCM
Prime Numbers and Prime Factors To study the highest common factor and lowest common multiple of a pair of numbers we first have to understand some of the basics. What is a FACTOR ? A number which divides wholly into another, leaving NO remainder. A number which can only be divided by ITSELF and ONE* What is a PRIME ? What is a PRIME FACTOR ? A number which is PRIME and a FACTOR of the number. To evaluate the HCF and LCM of a pair of numbers means that we have to have a GOOD understanding of prime numbers and prime factors. Before we look at HCF and LCM we will look at these more closely *Although the number 1 fits the definition, it is NOT regarded as a prime number. The first prime number (and the ONLY even prime number) is 2
Factors A number is a factor of another number if it divides wholly into the other number leaving NO remainder or fractional part. 1 2 3 4 5 6 7 8 9 10 11 12 12
Prime Numbers This table contains all of the prime numbers between 1 and 200. You will find it useful to try to memorise at least the primes up to 100.
Prime Factors To factorise a number using prime factors is done by dividing the number (and the result of that division) by the lowest prime, moving to the next suitable prime when the division stops. Sounds weird? Lets take a look at an example, this will clear up the confusion. 36 9 doesn t divide by 2 so we move to the next prime which is 3. We are left with 3, we stop here and list our prime factors.
Prime Factors We usually lay out the numbers as a sort of tree so you will hear the expression prime factor tree in your maths work. Here are a couple of prime factor trees
Hot Spot 1a Q1. Produce a prime factor tree for the number 56 56 56 2 28 2 14 2 7
Hot Spot 1b Q2. Produce a prime factor tree for the number 180 180 2 90 2 45 3 15 3 5
Lowest Common Multiple The LCM is the LOWEST number that is a multiple of two numbers. Example - Find the LCM of the numbers 6 and 8 Common factors are counted only once so the LCM of 6 and 8 is 24
Lowest Common Multiple The LCM is the LOWEST number that is a multiple of two numbers. Example - Find the LCM of the numbers 8 and 12 Common factors are counted only once so the LCM of 8 and 12 is 24
Hot Spot 2 Find the lowest common multiple of each of the following number pairs:
Highest Common Factor The HCF is a little easier to work out. We simply write out the factors of each of the pair and calculate the largest common factor in each list by expanding the common factors: Example: Find the HCF of 26 and 34
Highest Common Factor The HCF is a little easier to work out. We simply write out the factors of each of the pair and calculate the largest common factor in each list by expanding the common factors: Example: Find the HCF of 64 and 244
Highest Common Factor The HCF is a little easier to work out. We simply write out the factors of each of the pair and calculate the largest common factor in each list by expanding the common factors: Example: Find the HCF of 56 and 425 There are NO COMMON FACTORS between 56 and 425. In these cases the HCF is 1 as 1 is a factor of ANY number.
Hot Spot 3 Find the highest common factor of each of the following number pairs:
