in how many ways can 2310 be expressed as product of three factors??

1) 41
2) 56
3) 23
4) 46

• (3^(n-1)+1)/2
  2310=2*3*5*7*11
  n=5
  do this
  
  ans===41
• 10 years agoHelpfull: Yes(31) No(8)
• 2310 = 2*3*5*7*11....
  A product of 1st 5 prime numbers... 5 Factors!
  
  
  U need to take the product of 3 factors out of these 5 factors....
  Which can be taken in two ways.....
  {1 Factor}*{1 Factor}*{the rest 3 Factors}
  or {1 Factor}*{2 Factors}*{the rest 2 Factors}
  
  1st Case: There are 5*4 ways = 20 Ways
  2nd Case: There are 5*6(4C2) ways = 30 Ways
  
  A total of 50 ways in which 2310 can be expressed as a product of three factors....
• 10 years agoHelpfull: Yes(6) No(16)
• The Prime factors of 2310 are 2, 3, 5, 7 and 11, as 2310 = 2*3*5*7*11.
  Now, when 2310 is a product of three factors, two cases arise. (a) when 1 is one of the factors or the other case of two of the factors are 1's and (b) 1 is not one of the three factors.
  Lets consider each of the cases individually with examples.
  
  When two of the factors are 1's So, it should be 1 * 1* 2310. It can happen in only one way.
  When 1 is one of the factors, for example 1*11*210 , here as one of the factors is 1, the remaining 5 prime factors are to be divided into two groups. So, five numbers into two groups, it can be 4 and 1 or 3 and 2
  So, 1 * 4 factors * 1 factor - It can happen in 5 ways
  Or, 1 * 3 factors * 2 factors, this can happen in 5c3 = 10 ways
  
  Now the second case of 1 is not one of the factors,
  5 factors are to be divided into three groups, this can be
  
  3 factors * 1 factor * 1 factor- this can happen in 5c3 ways=10
  2 factors * 2 factors & 1 factor- this can happen in 5c2 * 3c2 = 30 ways
  
  Total = 1+5+10+10+30 = 56 ways
• 8 years agoHelpfull: Yes(3) No(6)
• 2310 = 2*3*5*7*11
  When a number can be expressed as a product of n distinct primes,
  then it can be expressed as a product of 3 numbers in (3^(n+1) + 1)/2 ways
• 11 years agoHelpfull: Yes(1) No(6)
• Ans:56
  1*1*2310
  1*2*(3*5*7*11)
  1*3*(2*5*7*11)
  1*5*(2*3*7*11)
  1*7*(2*3*5*11)
  1*11*(2*3*5*7)
  ...
  ...
  
• 9 years agoHelpfull: Yes(1) No(8)
• 1 is the ans
• 6 years agoHelpfull: Yes(0) No(1)
• 1 is the answer
• 5 years agoHelpfull: Yes(0) No(0)