Question about Factors and remainders

[weishao]

Factors:
You are given 2 numbers 68 and 297. How many unique factors does their product equal? <- what is the best approach to deal with questions like this? I can get their respective factors and then i guess i could cross check for duplicates but that is a bit time consuming...

Any other weird factor type hints are aprreciated.

Remainders:
Any tips on remainder questions where you have something like:
X is divide by 24 with remainder 13.
if X is multiplied by 30, what is the remainder?

Any other tips about remainders are appreciated..
I dont see these questions that often but they do appear maybe 1-4 times combined so it is definitely something i want to get it right when it comes...thanks

[venkata.jataprolu]

Factors:
You are given 2 numbers 68 and 297. How many unique factors does their product equal? <- what is the best approach to deal with questions like this? I can get their respective factors and then i guess i could cross check for duplicates but that is a bit time consuming...

Any other weird factor type hints are aprreciated.

Remainders:
Any tips on remainder questions where you have something like:
X is divide by 24 with remainder 13.
if X is multiplied by 30, what is the remainder?

Any other tips about remainders are appreciated..
I dont see these questions that often but they do appear maybe 1-4 times combined so it is definitely something i want to get it right when it comes...thanks

For you first question on factors,
A number m expressed as (a^p)*(b^q)*(c^r) where ^ represents, "to the power of" and * is multiplication, and a, b, c are all positive prime integers and p, q, r are all positive integers, the total number of factors of m will be (p+1)*(q+1)*(r+1).

For your second question, given X when divided by 24, leaves remainder 13.
X = 24p + 13, where p is the quotient of the division.
If X is multiplied by 30, (24p + 13)*30 will be RHS. 24(p*30) + (13*30). Now split 13*30 to be expressed as 24*16 + 6. The idea is to take 24 common as much as possible, that gives us 24(p*30) + 24*16 + 6. So, 24(p*30 + 16) + 6. Thus, 6 is the new remainder.