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  1. #1
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    factors

    Suppose that 9 and 14 are both factors of t. Can you be sure that 126 is a factor of t? EXPLAIN
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    Hello,
    Quote Originally Posted by j95snake1 View Post
    Suppose that 9 and 14 are both factors of t. Can you be sure that 126 is a factor of t? EXPLAIN
    Yes you can be sure Mainly because 9 and 14 are coprime (it means they have no common divisors - their gcd, greatest common divisor, is 1)

    The other problem is to explain. What is your level ? Have you ever dealt with divisibility proofs ?
    You can try to look here : http://www.mathhelpforum.com/math-he...ity-proof.html
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    we have not delt with the term coprime yet. I am in a basic college level class.

    does it mean that since 9 and 14 are factors of 126?
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    I also have this problem it is similiar.

    Suppose 9 and 12 are both divisors of m. Can you be sure that 108 is a divisor of m? EXPLAIN.
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    Quote Originally Posted by j95snake1 View Post
    we have not delt with the term coprime yet. I am in a basic college level class.

    does it mean that since 9 and 14 are factors of 126?
    It's because 9x14=126
    So if 9 and 14 divide any number t, then 9x14=126 divides this number t.

    It is not true for two numbers who have a common divisor, let's say... 4 and 6.
    4 and 6 divide 12, but 4x6=24 do not divide 12.

    I'll have to think about a proof... I don't remember learning it at such level

    I also have this problem it is similiar.

    Suppose 9 and 12 are both divisors of m. Can you be sure that 108 is a divisor of m? EXPLAIN.
    If you find that the two numbers have a common divisor, you can be SURE their product won't divide m (or t).

    Find a counterexample, that is in most case the lcm (least common multiple).
    The lcm of 9 and 12 is.. :
    9=3 \times 3
    12=3 \times 4
    The 3 in 12 is redundant.
    The lcm is 3 \times 3 \times 4=36

    9 and 12 divide 36.
    Does 9x12=108 divides 36 ?
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    Quote Originally Posted by j95snake1 View Post
    we have not delt with the term coprime yet. I am in a basic college level class.

    does it mean that since 9 and 14 are factors of 126?
    It's also known as "relatively prime"
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  7. #7
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    This problem is making me feel so dumb. I just dont understand what you have most likely explained right.
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