Number Properties Question

[baily106]

Hello,

I am referring to question #5 on page 51 of Book 4. The question reads "if j is divisible by 12 and 10, is j divisible by 24?" I read the explanation for this question. My question is this: when a question asks you is X divisible by Y and Z do you create factor trees separately or together? I feel in some cases one would put 12 and 10 and break it down to 2, 2, 2, 3, 5, but in this case it is 2, 2, 3 AND (separately) 2,5. How do you decide in which cases you do 2,2,2,3,5 factorization vice a 2,2,3 AND 2,5 factorization.

Thanks.

[tommywallach]

Hey Baily,

The rule is you don't count overlap twice. For example:

If j is divisible by 12 and 10

12: 223
10: 25

If you made a Venn diagram for this, there would be a 23 in the 12 circle, a 5 in the 10 circle, and a 2 in the overlap. This is what you count: 2325.

See how that works? The "2" that is in both circles is only counted ONCE.

-t

[baily106]

I believe I see the concept but will need to practice!
Thank you.

[tommywallach]

No problem. The best way to think of it is in terms of a Lowest Common Multiple, which you can always find by making a venn diagram of primes and counting all them (without double counting).

Good luck!

-t