



 
Madison, Find prime factors, then divide them out and try again with the quotient. If a number has no prime factor smaller than its square root it is prime. You should know that the first few primes are For a few of these there are easy tests: a number is divisible by 2 if its last digit is even Otherwise you need to use long division; for testing you may find it easier to keep only remainders. Once you have a list of prime factors expressed in the form "p_{i} occurs n_{i} times", systematically list every number with 0,1,...,n copies of p for each p.
Now try this yourself for 878. (You will have to try some larger primes, all in the list above, that can only be tested by long division. Your final list of factors should be quite short.) Good hunting!
 


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