Transcript Numbers Properties

Numbers Properties
• Learning Objective:
Recognise and use
multiples, factors,
common factor,
highest common
factor, lowest
common multiple and
primes; find the prime
factor decomposition
of a number
Must calculate the
Lowest common
Multiple of two
numbers
Should calculate the
HCF for two numbers
Could use HCF and
LCM to add and
subtract fractions with
different
denominators
Key Words
• Sequence, Term, nth term, consecutive,
predict, rule, generate, continue, finite,
infinite, ascending, descending, symbol,
expression, algebra, integer, index,
factors, multiples, square root, cube root,
HCF, LCM
Multiples
A multiple of a number is found by multiplying
the number by any whole number.
What are the first six multiples of 4?
To find the first six multiples of 4 multiply 4 by 1, 2, 3, 4, 5
and 6 in turn to get:
4,
8,
12,
16,
20
and
24.
Any given number has infinitely many multiples.
Multiples patterns on a
hundred square
The lowest common multiple
The lowest common multiple (or LCM) of two numbers is
the smallest number that is a multiple of both the numbers.
We can find this by writing down the first few multiples for both
numbers until we find a number that is in both lists.
For example,
Multiples of 20 are :
20,
40,
60,
80,
100,
Multiples of 25 are :
25,
50,
75,
100,
125, . . .
The LCM of 20 and 25 is 100.
120, . . .
WHY we need to know the lowest
common multiple
We use the lowest common multiple when adding and
subtracting fractions.
For example,
Add together 4
9
and 5 .
12
The LCM of 9 and 12 is 36.
4
9
+
×4
×3
5
16
12
×4
=
36
×3
+
15
36
=
31
36
Finding factors
A factor is a whole number that divides
exactly into a given number.
Factors come in pairs.
For example, what are the factors of 30?
1 and 30, 2 and 15, 3 and 10, 5 and 6.
So, in order, the factors of 30 are:
1, 2, 3, 5, 6, 10, 15 and 30.
The highest common factor
What is the highest common factor (HCF) of 24 and 30?
The factors of 24 are:
1
2
3
4
6
8
12
24
10
15
30
The factors of 30 are:
1
2
3
5
6
The highest common factor (HCF) of 24 and 30 is 6.
Why do we need to know the
highest common factor
We use the highest common factor when cancelling fractions.
For example,
Cancel the fraction 36 .
48
The HCF of 36 and 48 is 12, so we need to divide the
numerator and the denominator by 12.
÷12
36
48
=
÷12
3
4
Using prime factors to find the HCF
and LCM
We can use the prime factor decomposition to find the HCF
and LCM of larger numbers.
For example,
Find the HCF and the LCM of 60 and 294.
2
2
3
5
60
30
15
5
1
60 = 2 × 2 × 3 × 5
2
3
7
7
294
147
49
7
1
294 = 2 × 3 × 7 × 7
Using prime factors to find the
HCF
and
LCM
60 = 2 × 2 × 3 × 5
294 = 2 × 3 × 7 × 7
60
294
2
7
2
5
3
7
HCF of 60 and 294 = 2 × 3 = 6
LCM of 60 and 294 = 2 × 5 × 2 × 3 × 7 × 7 = 2940
Using prime factors to find the
HCF and LCM
Class Work
• Frameworking Pupil Book 3
• Exercise 1b Page 5 Question 1-10
Extension if your really good.