2310 can be expressed as product of 3 factors in how many ways?

• 2310=2*3*5*7*11
  take each single factor and combinaton of ramaining factor for eg 11:factors are:11*6*35,
  11*10*21,
  11*14*15..
  similarly for each factor we get 3 combinations
  so total ways=3+3+3+3+3=15
• 11 years agoHelpfull: Yes(11) No(5)
• 2310=2*3*5*7*11
  no of ways= 5C3 + 5C2*3C2 + 1= 41(ans)
  
• 11 years agoHelpfull: Yes(10) No(14)
• Just to explain Arun's solution:
  Factors are 2,3,5,7,11. We can group them in 2 ways: a group of 1,2,2 or a group of 1,1,3 factors
  for the first group choose as 5c2 and out of left 3 as 3c2. So 5c2*3c2
  for the sec group choose as 5c3 only (which is 5c3)
  I am unable to understand why 1 is added at last
• 11 years agoHelpfull: Yes(8) No(3)
• ans is 10...as we have 2*3*5*7*11
  and mke cobi to mke 3 factors so 5C3
  
• 11 years agoHelpfull: Yes(6) No(12)
• arun your answer is correct.Can u plzzzzzz explain how 5C2*3C2 and 1?
  plz do tell the concept
  
• 11 years agoHelpfull: Yes(5) No(2)
• 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
• 11 years agoHelpfull: Yes(4) No(3)
• 2310=2*3*5*11*7...so ans is 5c3+5c2*3c2(here you multiply 2 no and take other two)+1(for 210*1*1)=41
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• 11 years agoHelpfull: Yes(2) No(2)
• we cant take 5c3 because 2*3*1 or 5*3*7 and so on do not make 2310..
  ans is 5C2*3C2+1(for 2310*1*1)=31
  i think it is correct.
  
• 11 years agoHelpfull: Yes(2) No(2)
• 2310=2*3*5*7*11
  combinatons of factors are
  5C1*4C1*3C3=20
  5C1*4C2*2C2=30
  5C1*4C3*1C1=20
  5C2*3C1*2C2=30
  5C2*3C2*1C1=30
  5C3*2C1*1C1=20
  TOTAL no of ways = 20+30+20+30+30+20=150 ans...
• 10 years agoHelpfull: Yes(2) No(2)
• Ans:3^5=243
• 11 years agoHelpfull: Yes(1) No(6)
• ans is 5c3 2310=2*11*5*3*7.
  we have to find three distinct factors so we have to choose three out of 5 to make the combinations.
  
• 11 years agoHelpfull: Yes(0) No(6)
• ans: 15;
  1/2 * 5C2 * 3c2
  
  1/2 because we take 11,3 or 3,11 in combination..both result to same 33..
• 11 years agoHelpfull: Yes(0) No(4)
• its 5C3
  because we have 2310 = 2*3*5*7*11
  and we have to express it as a product of 3 factors. so its 5C3.
  
• 11 years agoHelpfull: Yes(0) No(2)
• why 1 is added please explain...:?????????
• 11 years agoHelpfull: Yes(0) No(1)
• we have 2310 as 2*5*3*7*11
  so now we should express as a product of 3 numbers then first lets take three numbers as
  2*3*5 now wee have 2 number remaining to get again 2310 as its product
  now this 2 numbers can be combined with 2 or 3 or 5 in 6 ways
  other condition for selecting 3 number
  this value of selection is 5c3 and now total is 6*5c3=60
• 11 years agoHelpfull: Yes(0) No(3)
• ans:
  2310 = 2*3*5*7*11
  here the factors of 2310 are different so we can write 2310 as product of
  (any of 5 factor)*(any from rest 4 factors)*(product of rest factors)
  
  this can be done in 5*4*1 = 20 ways
• 11 years agoHelpfull: Yes(0) No(2)
• 3 factors are 77*3*10
• 10 years agoHelpfull: Yes(0) No(0)