1. prime factorisation

Hi everyone,
I am about to start a computing course at a university. One of the 'modules' will obviously be mathematics. I'm not worried about the computing side of my studies. It's my maths that worries me. I will have to learn a lot. I started browsing the internet in search of some tutorials to refresh my memory and will probably have a lot of questions for you guys.

My first question is related to prime factorisation. How should I approach such a task? For example, I've got a number 1734 - how would I start analysing it to get:

1734 = 2 X 3 X 17^2

portia

2. 1734 is obviously divisible by 2. 2 is the first and only even prime.

1734/2=867.

This is not divisible by 2, so we choose the next prime that is. How about 3?

867/3=289.

Now, the next prime that divides into 289 is 17.

289/17=17

17/17=1 and we're done.

We have one 2, one 3, and two 17's

$\displaystyle 2\cdot 3\cdot 17^{2}$

Let's try another. Let's try 51894

51894/2=25947

25947/3=8649

8649/3=2883

2883/3=961

961/31=31

31/31=1

We have one 2, three 3's, and two 31's

$\displaystyle 2\cdot 3^{3}\cdot 31^{2}$

There, did that help?.

3. Thanks - it was very helpful.

Ok, so just to make sure I understand the rest:

we have got:

$\displaystyle 1734 = 2\cdot 3\cdot 17^{2}$

and

$\displaystyle 51894 =$$\displaystyle 2\cdot 3^{3}\cdot 31^{2}$

To find the Highest Common Factor we would multiply 2 and 3 because they appear as prime factors of both numbers.
LCM would then be:

$\displaystyle 2 \cdot 3^{2} \cdot 17^{2} \cdot 31^{2}$

Let's imagine a situation where we've got two sets of prime factors of some numbers:

1. $\displaystyle 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5$

2. $\displaystyle 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7$

Now, the HCF would be:

$\displaystyle 2 \cdot 2 \cdot 3 \cdot 3$

and LCM:

$\displaystyle 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5 \cdot 7$

Am I correct?

4. Yep. That's how you find a GCD and LCM. Different terminology for the same thing. Some use HCF, highest common factor, as you done. I reckon it depends on where one hails from.