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Math Help - HCF

  1. #1
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    HCF

    Has anyone got a quick way to find the Highest Common Factor (HCF) of these numbers?

    1). 6, 15
    2). 12, 16
    3). 12, 30
    4). 21, 14
    5). 36, 16
    6). 50, 35
    7). 45, 27
    8). 64, 88
    9). 35, 14
    10). 20, 40
    11). 28, 84
    12). 48, 84
    13). 99, 77
    14). 90, 36
    15). 60, 48
    16). 88, 66
    17). 96, 144
    18). 140, 252
    19). 175, 250
    20). 396, 252
    21). 27, 18, 99
    22). 42, 56, 98
    23). 108, 54, 90
    24). 96, 192, 144
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  2. #2
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    Quote Originally Posted by Natasha1 View Post
    Has anyone got a quick way to find the Highest Common Factor (HCF) of these numbers?

    1). 6, 15
    2). 12, 16
    3). 12, 30
    4). 21, 14
    5). 36, 16
    6). 50, 35
    7). 45, 27
    8). 64, 88
    9). 35, 14
    10). 20, 40
    11). 28, 84
    12). 48, 84
    13). 99, 77
    14). 90, 36
    15). 60, 48
    16). 88, 66
    17). 96, 144
    18). 140, 252
    19). 175, 250
    20). 396, 252
    21). 27, 18, 99
    22). 42, 56, 98
    23). 108, 54, 90
    24). 96, 192, 144
    Edit: You're asking far too many questions here, nobody will do all 24 for you. Especially if there is no evidence that you'd tried them yourself



    Split them into their prime factors and multiply the highest power of the factors which appear in both

    Eg 1:

    6 = 2 \times 3
    15 = 3 \times 5
    \text{HCF} = 3

    Eg 17

    96 = 2^5 \times 3
    144 = 2^4 \times 3^2
    \text{HCF} = 2^4 \times 3 = 48

    Note that I only multiplied by 2^4 because that is a factor of both
    Last edited by e^(i*pi); March 8th 2010 at 01:37 PM. Reason: see post
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  3. #3
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    Hello Natasha1
    Quote Originally Posted by Natasha1 View Post
    Has anyone got a quick way to find the Highest Common Factor (HCF) of these numbers?

    1). 6, 15
    2). 12, 16
    3). 12, 30
    4). 21, 14
    5). 36, 16
    6). 50, 35
    7). 45, 27
    8). 64, 88
    9). 35, 14
    10). 20, 40
    11). 28, 84
    12). 48, 84
    13). 99, 77
    14). 90, 36
    15). 60, 48
    16). 88, 66
    17). 96, 144
    18). 140, 252
    19). 175, 250
    20). 396, 252
    21). 27, 18, 99
    22). 42, 56, 98
    23). 108, 54, 90
    24). 96, 192, 144
    This is easier to do than to explain, but it's something like this:
    1. Find the prime factors of each number.

    2. For each prime factor that they have in common, choose the lower of their two exponents (powers).

    3. Multiply these common factors together.
    For instance, here's question 14, with the numbers 90 and 36:
    90 = 2^1\times3^2\times 5^1

    36 = 2^2\times 3^2
    The common prime factors are 2 and 3; the lower of their exponents then are:
    2^1 and 3^2
    So the HCF is 2^1\times 3^2 = 18.

    Did you follow that?

    Grandad
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  4. #4
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    Thanks for this but it's going to take me agesssssssssssssssssss :-(

    Can anyone do this on a computer and give me the answers please
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  5. #5
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Natasha1 View Post
    Thanks for this but it's going to take me agesssssssssssssssssss :-(

    Can anyone do this on a computer and give me the answers please
    I sure can, but I'm not going to. Surely if you wanted the answers you could google them or use wolfram...
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  6. #6
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    oh man! Harsh!!!

    What is Wolfram
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  7. #7
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    Quote Originally Posted by Natasha1 View Post
    oh man! Harsh!!!

    What is Wolfram
    Perhaps, and my apologies if I offended you. I stand by what I said though, I understand these problems and I've got plenty to do.

    Wolfram: Wolfram|Alpha although it doesn't seem to like prime factord
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  8. #8
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    Quote Originally Posted by e^(i*pi) View Post
    Perhaps, and my apologies if I offended you. I stand by what I said though, I understand these problems and I've got plenty to do.

    Wolfram: Wolfram|Alpha although it doesn't seem to like prime factord
    Great site thanks for the tip :-)
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