the numbers are from 31-39.

31, 32, 33, 34, 35, 36, 37, 38, 39

right away 31 can be eliminated and so can 37 because they are prime numbers

32 has only 1 prime factor= 2 X

33 has 2 prime factors=3 and 11 add them to get 14 X

34 has 2 prime factors=2 and 17 X

35 has 2 prime factors=5 and 7 add them to get 12 it works so thats ur answer.

2. there is a trick for the number of factors a number has. the trick is to factor the whole thing by using prime factorization

for example lets try the numbers 16, 20, 25, 30

note: they HAVE to be prime factorized

add 1 to all the exponents and multiply each of the exponents by one another if there is more than one

16=2^4 4+1=5 5 factors: 1,2,4,8,16

20=2^2 * 5^1 2+1=3 1+1=2 2*3=6 factors=1,2,4,5,10,20

25=5^2 2+1=3 factors=1,5,25

30=2^1*3^1*5^1 1+1=2 2*2*2=8

notice that the square numbers all have an odd number of factors such as 16 and 25. 16 is 4^2 and 25 is 5^2. neat trick huh?

so only square numbers can hav odd # of factors.

one more thing. since the sum of two prime numbers there is 5 the only 2 prime numbers that add up to five are 2 and 3. so the only 2 prime factors hav to be 2 and 3

the squares between 50 and 310 are: 64, 81, 100, 121, 144, 169, 196, 225, 256, and 289

since they need to have 2 as a factor get rid of the odd numbers

remaining: 64, 100, 144, 196, 256

get rid of the ones who dont have 3 as a factor

remaining: 144.

the answer is 144.

if u meant 31-50 its 36 because u get rid of the odds and the non multiples of 3 to get

36, 42, 48. 36 is the only square number here

3. the only 2 prime factors that multiply to 6 is 2 and 3.

17-29 take out odd and non multiples of 3

18=1,2,3,6,9,18

24=1,2,3,4, 6, 8,12, 24

strangely…they both work! because their only 2 prime factors are 2 and 3. which multiply to 6

IF THIS WAS TOO LONG TO READ HERE ARE THE ANSWERS

1. 35

2. 144 if u meant from 50-310. its 36 if u meant from 31-50

3. 18 or 24

2)There are several numbers between 310 and 50 which fall under this category. I’m assuming you meant between 31 and 50, in which case the answer is 48. Whatever the answer is, the prime factors are 2 and 3.

3) 24 (prime factors are 2 and 3).

srry i cant think of the others