what is the total number of factor of 16!

• 16! = 2^15 * 3^6 * 5^3 * 7^2 * 11^1 * 13^1
  
  total number of factors = (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1) = 5376
• 9 years agoHelpfull: Yes(48) No(5)
• @utkarsh and jaya krishna: write 16! interms of the prime factors,
  i.e 16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
  i.e 2^15* 3^12* 5^3*7^2*11^1*13^1
  and total no of factors formula is powers of prime factors incremented by 1 , their product
  ie (15+1)(6+1) (3+1)(2+1)(1+1)(1+1)=5376
• 9 years agoHelpfull: Yes(11) No(0)
• we need to write 16! in terms of their prime factors,
  now 16!= 16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
  i.e 2^15* 3^6* 5^3*7^2*11^1*13^1
  and total no of factors formula is powers of prime factors incremented by 1 and then their product
  i.e. (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)=5376
• 9 years agoHelpfull: Yes(7) No(0)
• 16/2=8
  8/2=4
  4/2=2
  2/2=1
  
  The no of factors are 8+4+2+1=15
• 9 years agoHelpfull: Yes(5) No(9)
• 16!=16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
  go for prime nos... which are 2,3,5,7,11,13
  Now power concerns ...
  power of 2 ...
  16/2=8
  8/2=4
  4/2=2
  2/2=1 ....sum 8+4+2+1=15 similarly for the rest one
  16!=2^15* 3^12* 5^3*7^2*11^1*13^1
  Total number of factors = (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1) = 5376
  I hope this gonna help u
  
  
• 9 years agoHelpfull: Yes(5) No(0)
• Ans:5376
  
  (2^15)*(3^6)*(5^3)*(7^2)*11*13
  (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)=16*7*4*3*2*2=5376
• 9 years agoHelpfull: Yes(3) No(0)
• i.e 16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
  so (2^15)*(3^6)*(5^3)*(7^2)*11*13
  (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)=16*7*4*3*2*2=5376
• 9 years agoHelpfull: Yes(2) No(0)
• how 15,6,3,2,1,1 came
• 9 years agoHelpfull: Yes(2) No(0)
• how you take 2^15 expression @rakesh
• 9 years agoHelpfull: Yes(1) No(0)
• there are 5 factors for 16 and they are 1,2,4,8,16
• 9 years agoHelpfull: Yes(1) No(5)
• no of factors=27
• 9 years agoHelpfull: Yes(1) No(2)
• total number of factors is the total number of prime numbers between 1 and 16
  1,2,3,5,7,11,13
  ans 7
• 9 years agoHelpfull: Yes(1) No(3)
• 7 ,,,,,,,,,,,,,,,,,,,,,,,,,,,bcoz 1 ,2, 3 ,5 and prime no.'s 7,11 and 13 are the factors of 16factorial
• 9 years agoHelpfull: Yes(0) No(3)
• not geting clearly,plz. explain me how to do this kind of problems..
• 9 years agoHelpfull: Yes(0) No(0)
• it can be written as
  (((10*10*10)/(12*12*12))+((9*9*9)/(12*12*12)))^1000
  now
  10/12=remainder is -2
  9/12=remainder is -3
  then,
  we can write
  ((-2*-2*-2)+(-3*-3*-3))^1000
  =(-35)^1000
  which means 1^1000
  so the remainder is 1
• 9 years agoHelpfull: Yes(0) No(0)
• 16=2*2*2*2*2
  16/2+16/4+16/8+16/16=15
  no of factors=15+1=16
• 9 years agoHelpfull: Yes(0) No(0)