# Thread: factors

1. ## factors

Suppose that 9 and 14 are both factors of t. Can you be sure that 126 is a factor of t? EXPLAIN

2. Hello,
Originally Posted by j95snake1
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

3. 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?

4. 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.

5. Originally Posted by j95snake1
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 ?

6. Originally Posted by j95snake1
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"

7. This problem is making me feel so dumb. I just dont understand what you have most likely explained right.