SOLUTION: what are the divisible numbers to 2367

Question 539753: what are the divisible numbers to 2367

Found 2 solutions by AnlytcPhil, KMST:
Answer by AnlytcPhil(1806) (Show Source): You can put this solution on YOUR website!
2367 = 3�3�263
Its divisors are 1, 3, 9, 263, 789, and 2367
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
What are the factors of 2367? The numbers that divide 2367 evenly? The divisors of 2367?
Since the digits add up to a multiple of 9 (3+6=9 and 2+7=9), 2367 is divisible by 9. When we divide it by 9, we get 263.
We look for prime numbers that will be divisors of 263.
It's not even, so 2 does not work.
It is not divisible by 3, because the digits do not add to a multiple of 3 (2+6+3=11).
If does not end in 5 or 0, so it's not divisible by 5.
The next prime number is 7, and my calculator says 263 divided by 7 is not a whole number.
The next prime number is 11, and does not work either. (There is an easy test for divisibility by 11, and 263 does not pass that test).
The next prime number is 13, and my calculator says that 263 divided by 13 is not a whole number either.
The next prime number is 17, but and that tells me I should stop here.
If 263 was 17 times some other number, that other number would have to be smaller than 17. If not prime, it would have a smaller prime divisor that should also divide 263. However, we could not find any prime divisor for 263 below 17, so 263 is a prime number.
The prime factorization of 2367 is
The factors (divisors) of 2367, in pairs are
1 and 2367 2637=1*2367
3 and 7101 2367=3*7107=3*3*263
9 and 263 2367=9*263
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