# Product of Prime (MATHS)

Useful and shows a clear method.

Teacher recommended

- Created by: gogos
- Created on: 20-06-10 18:33

## Slides in this set

### Slide 1

www.powerpointmaths.com © Where quality comes first!

PowerPointmaths.com © 2004 all rights reserved…read more

### Slide 2

Prime and Composite Numbers

The positive integers (excluding 1) can be divided into two sets.

1 2 3 4 5 6 7 8 9 10

primes

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

composites

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50 All composite numbers can

be expressed as a product

51 52 53 54 55 56 57 58 59 60 of primes. For example:

61 62 63 64 65 66 67 68 69 70 55 = 5 x 11

71 72 73 74 75 76 77 78 79 80

70 = 2x5x7

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100 90 = 2 x 32 x 5

You may be familiar with these from the Sieve of Eratosthenes.…read more

### Slide 3

M1

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 1: Write 180 as a product of primes.

None of these factors are prime so re-write them

180 = 10 x 18 as a product of smaller factors and keep

repeating if necessary until all factors are prime.

180 = 2 x 5 x 3 x 6

All factors are now prime so re-write

180 = 2 x 5 x 3 x 2 x 3 in ascending order as powers.

180 = 22 x 32 x 5 When written in this way we say that

it is expressed in canonical form.…read more

### Slide 4

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 2: Write 200 as a product of primes.

None of these factors are prime so re-write them

200 = 10 x 20 as a product of smaller factors and keep

repeating if necessary until all factors are prime.

200 = 2 x 5 x 4 x 5

2 All factors are now prime so re-write

200 = 2 x 5 x 2 x 5 in canonical form.

200 = 23 x 52…read more

### Slide 5

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 3: Write 84 as a product of primes.

84 = 7 x 12

84 = 7 x 3 x 4

84 = 7 x 3 x 22

84 = 22 x 3 x 7…read more

### Slide 6

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 4: Write 144 as a product of primes.

144 = 12 x 12

144 = 3 x 4 x 3 x 4

144 = 3 x 22 x 3 x 22

144 = 24 x 32…read more

### Slide 7

### Slide 8

### Slide 9

### Slide 10

## Related discussions on The Student Room

## Similar Mathematics resources:

# Product of Prime (MATHS)

Useful and shows a clear method.

Teacher recommended

- Created by: gogos
- Created on: 20-06-10 18:33

## Slides in this set

### Slide 1

www.powerpointmaths.com © Where quality comes first!

PowerPointmaths.com © 2004 all rights reserved…read more

### Slide 2

Prime and Composite Numbers

The positive integers (excluding 1) can be divided into two sets.

1 2 3 4 5 6 7 8 9 10

primes

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

composites

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50 All composite numbers can

be expressed as a product

51 52 53 54 55 56 57 58 59 60 of primes. For example:

61 62 63 64 65 66 67 68 69 70 55 = 5 x 11

71 72 73 74 75 76 77 78 79 80

70 = 2x5x7

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100 90 = 2 x 32 x 5

You may be familiar with these from the Sieve of Eratosthenes.…read more

### Slide 3

M1

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 1: Write 180 as a product of primes.

None of these factors are prime so re-write them

180 = 10 x 18 as a product of smaller factors and keep

repeating if necessary until all factors are prime.

180 = 2 x 5 x 3 x 6

All factors are now prime so re-write

180 = 2 x 5 x 3 x 2 x 3 in ascending order as powers.

180 = 22 x 32 x 5 When written in this way we say that

it is expressed in canonical form.…read more

### Slide 4

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 2: Write 200 as a product of primes.

None of these factors are prime so re-write them

200 = 10 x 20 as a product of smaller factors and keep

repeating if necessary until all factors are prime.

200 = 2 x 5 x 4 x 5

2 All factors are now prime so re-write

200 = 2 x 5 x 2 x 5 in canonical form.

200 = 23 x 52…read more

### Slide 5

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 3: Write 84 as a product of primes.

84 = 7 x 12

84 = 7 x 3 x 4

84 = 7 x 3 x 22

84 = 22 x 3 x 7…read more

### Slide 6

The Fundamental Theorem of Arithmetic

Every positive integer (excluding 1) can be expressed as a product of primes and

this factorisation is unique (Euclid IX.14).

To write a number as a product of primes first write it as a product of

any two convenient factors.

Example 4: Write 144 as a product of primes.

144 = 12 x 12

144 = 3 x 4 x 3 x 4

144 = 3 x 22 x 3 x 22

144 = 24 x 32…read more

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