1. Where might prime numbers be used?
Discuss with the people on your table how maths is used in these digital careers?
Challenge:
Where might prime numbers be used?

2. Where might prime numbers be used? Cyber security in banks
Square and cube numbers
Prime factor decomposition
Percentages and interest
Vectors
Transformations of shapes
Substitution in algebraic formulas
Discuss with the people on your table how maths used in these digital careers?
Challenge:
Where might prime numbers be used? Cyber security in banks

3. Agree Learning Objectives.
WE ARE LEARNING… Prime Decomposition
THINGS TO REMEMBER...
Prime numbers have only 2 factors 1 and itself.
YOU WILL BE ABLE TO… All will be able to use a Factor tree to decompose a number into Primes Most will be able to confidently write the answer in Index Notation Some will be able to spot the pattern in the decomposition of Square numbers
TRIC… Focussed
Key Words.
Prime, Decomposition, product P C A R

4. Agree Learning Objectives
WE ARE LEARNING…Prime Decomposition
YOU WILL BE ABLE TO…
All will be able to use a Factor tree to decompose a number into Prime
Most will be able to confidently write the answer in Index Notation
Some will be able to spot the pattern in the decomposition of Square numbers
THINGS TO REMEMBER...Prime numbers have only 2 factors 1 and itself.
Key Words…Prime, Decomposition, Product

5. L.O. To break numbers down into products of their primes
13 November, 2018
Prime Decomposition
L.O. To break numbers down into products of their primes

6. Present new Information
If you use internet banking, you want it to be secure
Banks will code your data using a very long number which is the product of 2 primes
You will have a Prime number assigned and the bank will have another

7. Present new Information
These are multiplied together to get the code
Even if people hacking the data get the code, they will be unable to get the 2 prime numbers given to you and the bank (which would be needed to get your money!)
This is because the numbers used are so big, a supercomputer would still take years to break it down (The primes used will have over 200 digits each)
Banks change codes every now and then, which effectively resets the process!

8. Present new Information
‘Prime Decomposition’
What does this mean?
Prime = Prime numbers
Decomposition = Breaking down
What we will be doing is breaking down bigger numbers into ‘products’ of their Prime factors.
This is done using a ‘factor tree’

9. Present new Information
Write 120 as a product of its prime factors
120 2 60 2 30 2 15 3 5
120 = 2 x 2 x 2 x 3 x 5
= 23 x 3 x 5

10. Present new Information
‘Prime Decomposition’
Write 80 as a product of its prime factors 2 40 2 20 2 10 2 5
80 = 2 x 2 x 2 x 2 x 5
= 24 x 5

11. Draw a factor tree for the following numbers:
Construct Meaning
Draw a factor tree for the following numbers:
A) 64
B) 250
C) 164

12. Draw a factor tree for the following numbers:
Construct Meaning
Draw a factor tree for the following numbers:
A) 64 = 26
B) 250 = 2x53
C) 164 = 22 x 41

13. Apply to demonstrate
Bronze: Using factor trees to break down numbers into their prime factors
Silver: Spotting patterns between the prime factorisation of numbers and their squares.
Gold: Problem Solving: Using very large numbers that are not prime to factorise – much like cyber security experts do for banks.

14. More challenging numbers
Bronze Prime decomposition
More challenging numbers

15. More challenging numbers
Bronze Prime decomposition
22 x 5 52
22x3x5
2x32
22x52
23x5
24x5
25x5
Because they are doubled the power of two increases by one
More challenging numbers
5x31
2x3x5x7
24x3x52
3x52x7
e) 3x41
f) 29
g)210
h) 211

16. Silver Prime decomposition

17. Silver Prime decomposition
2x3
2x5
22x3
22x5
22x32
22x52
24x32
24x52

18. Gold Prime decomposition

19. Gold Prime decomposition
11x17
23x29
37x89
653x761

20. Present new Information
HCF
Highest common factor
Biggest
Same
number that goes into it
LCM
Lowest common Multiple
Smallest
Same
number in the times tables

21. Present new Information
Find the HCF of 60 and 70 70 60 2 30 2 35 2 15 5 7
70 = 2 x 5 x 7 3 5
= 2 x 5 x 7
60 = 2 x 2 x 3 x 5
= 22 x 3 x 5
HCF = 2 x 5 = 10

22. Find the HCF and LCM of these numbers using prime factor trees
Apply to Demonstrate
BRONZE
Find the HCF and LCM of these numbers using prime factor trees
6 and 15
20 and 30
14 and 42

23. Apply to Demonstrate BRONZE HCF =3, LCFM =30 HCF =10 LCM =60

24. Review
Write a summary using less than 15 words on what prime decomposition is and how to do it. You can use as many numbers and symbols as you like.

25. To watch a clip about careers in the digital sector click here:
=CImBfuAeKd8
For further information, please see resources/