please can someone explain to me what are factors and prime factors?

[ssd]

am trying to help ds with homework and my brain is much

thanks!

mush!

factors are numbers that go into another number for example factors of 12 are, 1,2,3,4,6,12

prime numbers have no other numbers that go into them apart from 1 and the number eg 7,13,19

thank you!

so whats the prime factor of 128? is it 1 and 128?

And prime factors are the prime numbers which when multiplied together give you the number e.g. the prime factors of 10 are 2 and 5

the prime factor of 128 is both a prime number, and a factor of 128

this is 2 as 2 divides into 128, and is a prime number

no - 128 is not a prime number.

Have a look here

sorry, I'm not saying 128 is a prime number, I am saying that 2 is a prime number, and 2 is the prime factor of 128

it is 2 to the power of 7 ie 2x2x2x2x2x2x2

OP asked for the prime factor of 128, and it is 2, I didn't want to confuse her with explaining about how to expres a number as the product of its prime factors as that is not waht she was asking - but I probably wasn't very clear - sorry!

thanks I'm still confused, think I'm just thick at maths!

Basically a factor is a number you can divide a given number into a whole number of times.

So if your number is 6 you can divide it by 1 or 2 or 3 or 6. These are all factors of 6. But you can not divide it by 4 or 5 a whole number of times so 4 & 5 are not factors of 6.

A prime number is a number that is only divisible by 1 and itself. 1, 2, 3, 5, 7, 11, 13 etc Your dc probably knows this sequence already.

So in my example of the number 6 - the prime numbers in the list of factors I've identified are 1, 2 and 3. Leaving six out of the answer as it is not a prime number.

In your question where you need to find the prime factors for 128 I would do it the other way round. ie use the prime number list to see if any of those are a factor of 128.
So 1 and 2 are, but 3 isn't as it doesn't divide by a whole number of times. (128/3 = 42.666)

The point is that the prime factorisation of a number is unique: there's only one way to express a given number as the product (multiplying together) of a list of prime numbers. A prime is a number greater than one that cannot be divided by any integer other than itself without a remainder: 2 3 5 7 11 13 17. Contrary to what others have said, 1 is not prime: see here for why, but as a warning it's fairly technical within a few paragraphs. The main reason 1 isn't prime is because it breaks the uniqueness property. If 1 were prime, you could factor six as 2.3, 1.2.3, 1.1.2.3, 1.1.1.2.3 and so on.

So the prime factors of 128 (a bad example because it confuses things) are 2 2 2 2 2 2 2 because you can make 128 by multiplying seven twos together. As a better example, the prime factors of 6 are 2 and 3. End of.

There are no "fast" methods to determine the prime factors of a given number (see here). It's one of the open problems of mathematics, and fame awaits any serious progress in the area.

In a nutshell factors are the numbers that will go into another number ie the factors of 12 are 1 and 12 (1x12=12),2 and 6 (2x6=12) and 3 and 3 (3x4=12)

Prime numbers are numbers with no factors other than 1 and themselves eg 13 (you can only make 13 by 1x13)
Prime factors are factors that prime numbers. 1 is not prime though.
So the prime factors of 12 are 2 and 3 (not 1, not 4 as this is divisible by 2 and not 6 or 12 as these are divisible by 2,3,4 and 6)
Easiest way to find them is to start with 2 and keep going...
12 divided by 2 = 6. 6 isn't prime so divide by 2 again. 6 divided by 2 = 3 which is prime. So answers are 2 and 3.
It's easier to show with tree diagrams but can't do them here, look at bbcbitesize for help.

"Easiest way to find them is to start with 2 and keep going..."

Find a substantially better way and you'll make Einstein look like a minor figure who did a bit of physics.

My point is some people try 2, then 3, then 5 and so on until they have tried all the numbers up to their target rather than halving over and over.