Suppose that 9 and 14 are both factors of t. Can you be sure that 126 is a factor of t? EXPLAIN
Hello,
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
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
If you find that the two numbers have a common divisor, you can be SURE their product won't divide m (or t).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.
Find a counterexample, that is in most case the lcm (least common multiple).
The lcm of 9 and 12 is.. :
$\displaystyle 9=3 \times 3$
$\displaystyle 12=3 \times 4$
The 3 in 12 is redundant.
The lcm is $\displaystyle 3 \times 3 \times 4=36$
9 and 12 divide 36.
Does 9x12=108 divides 36 ?