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6 votes
6 votes
My number is a multiple of 4. My number has 8 factors, including 2 and 3. My number is less than 30. My number is​

User Esdef
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2 Answers

13 votes
13 votes

Answer:

24

Explanation:

mutiples of fours under 30 leave 7 possible numbers

but the only number w 8 factors under 30 is 24

User Patrick Gunderson
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21 votes
21 votes

(if you're too lazy to read all of the below im about to say then because it is divisible by 2,3,4 and less than 30 the number is 2 x 3 x 4 = 24)

First, we exclude 0 cause it has more than 8 factors (literally)

Since 2 and 3 are 2 of the number's factors, it must be divisible by 6.

Therefore, we have 4 options : 6,12,18,24 (30 does not count)

Since it is divisible by 4, we are left with 2 : 12 and 24.

(here's something extra which is how to identify the number of factors a number has, not necessary in this case cause we can just count, but it's useful anyways)

We do the prime factorization of that number :
For example : 120
The prime factorization of 120 is 2^3 x 3 x 5.
Now, we take the index number of every single one of the prime numbers in the factorization, add each of them by 1 and multiply them

So, the index number of 2 is 3, 3 is 1 and 5 is 1 (2^3 x 3^1 x 5^1)
-> 120 has (3+1)(1+1)(1+1) = 16 (factors).

Applying it to this case, only 24 would work, as :
24 = 3 x 2^3
So, it has (3+1)(1+1) = 8 (factors), just as it says.

User Robgraves
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