what is the total no of factors of 16!?

• 16!=1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16
  =2*3*2*2*5*2*3*7*2*2*2*3*3*2*5*11*2*2*3*13*2*7*3*5*2^4
  2^15*3^6*5^3*7^2*11*13
  So no. Of factor =16*7*4*3*2*2
  =448*12
  = 53 76
• 10 years agoHelpfull: Yes(30) No(2)
• ==>1* 2* 3* 4* 5 *6 *7 *8 *9 *10 *11* 12* 13 *14* 15 *16
  
  ==>(2^15)*(3^6)*(5^3)*(7^2)*(11^1)*(13^1)
  total no of factors=>(15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)
  =>16*7*4*3*2*2
  [ans==>5376]
• 10 years agoHelpfull: Yes(12) No(0)
• this question can be solved based on splitting the numbers into basic co-primes. to split a number as possible into the co primes.
  for 16!
  2*3*......15*16
  to split number based on coprimes
  (2^15)*(3^6)*(5^3)*(7^2)*(11^1)*(13^1)
  ie: (x^n)*(y^n) so the no of factors are (n+1)*(n+1)
  16*7*4*3*2*2
  =5376
• 10 years agoHelpfull: Yes(6) No(0)
• 5376
  1* 2* 3* 4* 5 *6 *7 *8 *9 *10 *11* 12* 13 *14* 15 *16
  
  (2^15)*(3^6)*(5^3)*(7^2)*(11^1)*(13^1)
  total no of factors=(15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)
  16*7*4*3*2*2
  [ans 5376
• 10 years agoHelpfull: Yes(2) No(0)
• 16!=1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16
  =2*3*2*2*5*2*3*7*2*2*2*3*3*2*5*11*2*2*3*13*2*7*3*5*2^4
  2^15*3^6*5^3*7^2*11*13
  So no. Of factor =16*7*4*3*2*2
  =448*12
  = 5376
• 10 years agoHelpfull: Yes(2) No(0)
• guys why have u multiplied the number of factors. it is asked to find the total number of factors n 16!. shouldn't we add the number of factors to get the total number of factors????
• 10 years agoHelpfull: Yes(1) No(7)
• 16!= 2^15 * 3^6 * 5^3 * 7^1 * 13^1 where 2,3,5,7,13 are the prime no. less then 16 then total number of factors is equal to 16*7*4*2*2
• 10 years agoHelpfull: Yes(0) No(2)
• 2^15*3^6*5^3*7^2*11^1*13^1 i.e
  a^p*b^q.................z^r
  then
  total factors=(p+1)*(q+1)...............
  so
  16*7*4*3*2*2=5376
• 10 years agoHelpfull: Yes(0) No(1)
• 17 factors are there in 16! i.e 1,2......16 and 16! itself
• 10 years agoHelpfull: Yes(0) No(8)