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Prime Factorisation
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Prime Factorisation

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Prime Factorisation

AKA the Unique Factorisation Theorem, we can split any number down into a product of prime numbers, where each number has one unique combination!

1

A factor is a number that divides into another number exactly. Which of these numbers is a factor of 2828?

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2

Because 28÷7=428\div 7=4 we know that 77 is a factor of 2828.

It also shows that 44 is a factor of 2828 because 28÷4=728\div 4=7.

1

We have seen that 44 and 77 are factors of 2828. A prime factor, is a factor that is a prime number. Which one of these is a prime factor of 2828?

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2

We have found two factors of 2828 and found that 77 is a prime factor. What other factors are there are of 2828? Select all that apply.

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You can select multiple answers

3

We now have all the factors of 2828.

They are 11, 22, 44, 77, 1414 and 2828.

1

Finding all the factors of a number can be quite tedious.

We can use a process called prime factorisation to help.

2

We have seen that all the factors of 2828 are 11, 22, 44, 77, 1414 and 2828. Which of these are prime? Select two and separate your answer with a comma.

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3

We have now found the prime factors of 2828, they are 22 and 77. Which calculation uses those factors to make 2828?

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4

We have found the prime factorisation of 2828 which is 2×2×72\times 2\times 7.

Note that sometimes a prime factor is repeated.

5

Prime number factorisation helps us in other areas of maths.

If can help us to find common multiples and factors which in turn help working with fractions.

1

Let's use a prime factor tree to find the prime factors of a number.

We will identify the prime numbers as they appear.

2

Starting with 2828, we find a factor. We start with 44 and put that in the next tier. What number will replace the ???

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3

We now look at our factors and determine if either of them is prime.

We know that 77 is prime, so we circle it to show it is the end of that branch.

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4

We now focus on the number 44. What number is a factor of 44 that can replace both the question marks?

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5

We have replaced the ?? with the number 22.

We know that 22 is prime so circle them both.

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6

We now have the prime factorisation of the number 2828.

Take the circled prime numbers and multiply them together: 2×2×7=282\times 2\times 7=28

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1

Let's find the prime factorisation of 1616. If the first factor is 22, what number completes this stage of the tree?

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2

We've added 88 which also has a factor of 22. What completes this stage of the tree?

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3

Circle the prime numbers as you go. What number completes this tree?

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4

This is our completed tree for the prime factorisation of 1616.

We bring this together by multiplying the prime factors so we have 2×2×2×2=162\times 2\times 2\times 2=16.

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5

It's not the only way to draw a factor tree for 1616

Instead, we could start by splitting 1616 into 4×44 \times 4.

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6

What's the prime factorisation now?

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7

The two trees are different but the final answer is still the same.

Every composite number has a unique prime factorisation.

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1

We have seen that the prime factorisation of 1616 is 2×2×2×22\times 2\times 2\times 2.

We can shorten this using the fact that powers of a number are repeated multiplication.

2

There are four 2s2s in the expression 2×2×2×22\times 2\times 2\times 2. Keeping 22 as the base number, what is the power we need to use?

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3

This gives an alternative way of writing the prime factorisation of 1616.

24=162^4=16

Quick recap: what is prime factorisation and why is it helpful? Select all the options that apply.

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You can select multiple answers

What is the prime factorisation of 3636? Take some time to work this out if you need to

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We have seen that the prime factorisation of 3636 is 2×2×3×32\times 2\times 3\times 3. What is an alternative way of writing this?

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Final question! Use prime factorisation to express 5454 as the product of its prime factors. Keep the factors in number order in your answer.

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Summary!

1

A factor is a number which divides exactly into another number with no remainder or decimal answer.

44 is a factor of 1212 as 12÷4=312\div 4=3

55 is not a factor of 1212 as 12÷5=2.412\div 5=2.4

2

A prime factor is a factor that is a prime number.

44 is a factor of 1212 but it is not a prime factor

33 is a prime factor of 1212

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3

Every number has a unique prime factorisation

The prime factorisation of 1212 is 2×2×32\times 2\times 3 or 22×32^2\times 3.

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4

Use a prime factor tree to find the prime factorisation of a number.

Prime factorisation of 2828 is 2×2×72\times 2\times 7 or 22×72^{2}\times7

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