Wikipedia:Reference desk/Archives/Mathematics/2019 June 29

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June 29

Factors

What are factors of 12 — Preceding unsigned comment added by 41.115.7.17 (talk) 11:39, 29 June 2019 (UTC)

A "factor" is a whole number that divides perfectly into another whole number. For example, 5 divides perfectly into 15, so 5 is a factor of 15. So all you have to do is make a list of the whole numbers that divide perfectly into 12. Because this looks like a homework question, we can't give you much more help than this. I will start you off by pointing out that both 1 and 12 are factors of 12, because they both divide perfectly into it. There are four more factors of 12. Good luck finding them! RomanSpa (talk) 19:05, 29 June 2019 (UTC)

Here whole number is ment to mean positive whole number. Bo Jacoby (talk) 20:00, 29 June 2019 (UTC).

Obviously, the (positive and negative) divisors of 12 are ±1, ±2, ±3, ±4, ±6, and ±12. If you only want the positive divisors, then ignore the ± signs. GeoffreyT2000 (talk) 23:02, 29 June 2019 (UTC)

@GeoffreyT2000: Obviously ...to whom? Certainly not to OP! Your answer jumped out of the box, with no explanation why it is like this, and I don't think someone who asks such elementary question will make much use of such answer. BTW, you didn't read the answer by RomanSpa above, did you? --CiaPan (talk) 21:33, 30 June 2019 (UTC)

To find the number of factors of a number when its prime factorization is known, you can simply:

1. Factor it into primes.
2. Study the exponents. Include the 1's to prevent a mistake. For example 12's prime factorization is 2^2 times 3^1.
3. Add one to each exponent. 3 times 2 = 6.
4. Thus, 12 has 6 factors.

If you include negative factors (as GeoffreyT2000 did,) we simply multiply the above calculation by 2, and 6 times 2 equals 12. -- Georgia guy (talk) 23:57, 30 June 2019 (UTC)

@Georgia guy: Yes, that's correct. Possibly you meant to direct your reply to OP...? --CiaPan (talk) 10:59, 2 July 2019 (UTC)