factors and relation

[Guest]

PLease help!!1

the number(s) : 6, 8, 10, 14, and 15 all have four factors. I need to find a pattern in these number or i need to show how they are related. The same with 4, and 9 which both have 3 factors, and 18, and 20 which both have 6 factors

 

[pka]

First, I am not sure what the author of your question is looking for.
However, here is a fact about number of factors for any number.
The number \(\displaystyle \L
453,600 = 2^5 \cdot 3^4 \cdot 5^2 \cdot 7\) has (6)(5)(3)(2)=180 factors.
In general, the number \(\displaystyle \L
2^a \cdot 3^b \cdot 5^c \cdot 7^d\) has (a+1)(b+1)(c+1)(d+1) factors.

Write the number in its prime factorization form.
Add one to each positive exponent and multiply.
That is the number of factors.

 

[soroban]

Hello, bware!

The number(s) : 6, 8, 10, 14, and 15 all have four factors.
I need to find a pattern in these number or i need to show how they are related.
The same with 4, and 9 which both have 3 factors,
and 18 and 20 which both have 6 factors

Perhaps they expect you to notice that most numbers have an even number of factors,
\(\displaystyle \;\;\)and only squares have an odd number of factors.