Prime factors

We know Prime `=` Prime numbers 2, 3, 5, 7, 11, 13.............

We know Factors `=` Take a number apart using ladders

So logically Prime Factors are:

A prime factor is a prime number that multiplies into a larger number

Example 1

What is the prime factorization of 12?

Remember the prime number that go into my dog bites several KGB men

Factor the number 12

Write down the number and put two ladders up against it.

Draw 2 ladders below a number side by side

Then write the numbers from 1 down the left ladder.

On the first ladder start with one and ascend the numbers on each rung until you get to half the number you are trying to factorise

Now fill the right ladder with the numbers that multiply to give 12.

On the second ladder start with the number you are factorising and descend in 2's until you get to 2 match opposing rungs up, this will give you the factors of the number

Therefore the factors of 12 are:

1 and 12

2 and 6

3 and 4

Alternatively the factors of 12 are 1, 2, 3, 4, 6 and 12

Only 2 and 3 are prime factors of 12

The only prime numbers that are also factors of 12 are:

2 and 3

So we have to use only these two numbers to multiply to 12.

Try `2times3=6`

Try `(2times3=6)times2=12`

So the answer is `2times3times2`

or `2times2times3`

or `2^2times3`

Example 2

What are the prime factors of 24?

Use the phrase My dog bites several KGB men to remember the first six prime numbers by counting the letters in each word of the phrase

Fill out ladders 1 and 2 and take the prime factors

The prime factors of 24 is 2 and 3

The only prime numbers that are also factors of 24 are:

`2` and `3`

So we have to use only these two numbers to multiply to 24.

Try `2times3=6`

Try `(2times3=6)times3=18` - can't multiply to get 24

Try `(2times3=6)times2=12`

Try `(2times3times2=12)times2=24`

So the answer is `2times3times2times2`

which is `2times2times2times3`

or `2^3times3`

Example 3

What is the prime factorisation of 70?

Remember the prime number that go into my dog bites several KGB men

Factor 70

Fill in the ladders and take the factors of 70

The prime factors of 70 is 2, 5 and 7

The only prime numbers that are also factors of 70 are:

2, 5 and 7

So we have to use only these 3 numbers to multiply to 70

Try `2times5=10`

Try `(2times5=10)times7=70`

So the answer is `2times5times7`

Example 4

What is the prime factorisation of 147?

Use the phrase My dog bites several KGB men to remember the first six prime numbers by counting the letters in each word of the phrase
Factor 147

Factorise 147 using the ladder method

The prime factors of 147 are 3 and 7

NOTE:

21 and 49 are not prime numbers.

The only prime numbers that are also factors of 147 are:

3 and 7

So we have to use only these two numbers to multiply to 147.

Try `3times7=21`

Try `(3times7=21)times7=147`

So the answer is `3times7times7`

or ` 3times7^2`

Example 5

What is the prime factorisation of 17?

Use the phrase My dog bites several KGB men I laughed to remember the first seven prime numbers by counting the letters in each word of the phrase

Factor 17

There are no combinations of 17 so there are no prime factors either

There are no other combinations that work.

17 is a prime number.

So 17 is the prime factorisation.