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Math Help - prime factorisation

  1. #1
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    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


    thanks in advance
    portia
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  2. #2
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    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

    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

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

    There, did that help?.
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  3. #3
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    Thanks - it was very helpful.

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

    we have got:

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

    and


    51894 = 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:

     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.  2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5

    2.  2 \cdot 2 \cdot 3 \cdot 3 \cdot 7

    Now, the HCF would be:

    2 \cdot 2 \cdot 3 \cdot 3

    and LCM:

    2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5 \cdot 7

    Am I correct?
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  4. #4
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    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.
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