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Thread: Cheking divisibility by 36,32 and 24

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    Cheking divisibility by 36,32 and 24

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    I am only familiar with divisibility by 2,3,4,5,6,8,9,10,11 how do we check for 36,32,and 24 ?

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    For divisibility by any number that you haven't memorized a shortcut rule for, consider all the factors of that number and pick out a pair of two factors for which:

    a. you know a divisibility rule AND;
    b. their least common multiple is the number itself

    Here are some examples for those numbers:

    36's factors are 1, 2, 3, 4, 6, 9, 12, 18, 36. Well, 4*9 = 36 and their LCM is 36 so you have something to work with here. Check if the number is divisible by 4 and 9 and if it is, then it is divisible by 36 as well.

    32's factors are 1, 2, 4, 8, 16, 32. However, since the only prime factor of 32 is 2, there is no pair of factors for which the LCM is 32 (besides 32 and 1) so there is no shortcut divisibility rule for 32.

    24's factors are 1, 2, 3, 4, 6, 8, 12, 24. Well, 8*3 = 24 and their LCM is 24. Therefore, if the number is divisible by both 8 and 3, it's divisible by 24.
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    For 32: well, you can first quickly check if the number is divisible by 8, because if it's not then it definitely isn't divisible by 32. If it is, well, I find dividing a number by 2 is relatively easy. I would do that twice, then check to see whether the resulting number is divisible by 8.

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    Quote Originally Posted by mxplusb View Post
    For 32: well, you can first quickly check if the number is divisible by 8, because if it's not then it definitely isn't divisible by 32. If it is, well, I find dividing a number by 2 is relatively easy. I would do that twice, then check to see whether the resulting number is divisible by 8.
    mxplusb, kindly explain the rule that you have used to solve for 32.

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    32's factors are 1, 2, 4, 8, 16, 32. However, since the only prime factor of 32 is 2, there is no pair of factors for which the LCM is 32 (besides 32 and 1) so there is no shortcut divisibility rule for 32.
    DaveTutor, I've never heard of this rule that when a number has only one prime factor, then that number's any pair of factor's LCM cannot be that number. Please elaborate on that.

    Also, to find it for 30, we have factors 1,2,3,5,6,10,15,30. So here LCM of 2 & 15 and 3 and 10 is 30. So which pair be used?

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    It is not a rule, just an observation.

    32=8*2*2
    Therefore, any number that is divisible by 32 must also be divisible by 8
    so if it is not divisible by 8 it is not divisible by 32.

    Also dividing by 2 twice and then checking for divisibility by 8 is exactly equivalent to checking for divisibility by 32.

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    Divisibility by 32

    Quote Originally Posted by DaveTutor View Post

    32's factors are 1, 2, 4, 8, 16, 32. However, since the only prime factor of 32 is 2, there is no pair of factors for which the LCM is 32 (besides 32 and 1) so there is no shortcut divisibility rule for 32.
    Actually, there is a rule for 32, just check if the last 5 digits are divisible by 32. This is reinforced by another rule that states that you can find if any number is divisible by 2^n by checking if the last n digits is divisible by 2^n.

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