The prime factorization of 1995, which is 3*5*7*19, uses each odd digit exactly one and 1995 is the smallest positive integer with this property. What is the next smallest?
Please show steps for solving.
Sorry, I don't understand your question!!. ALL prime factors of any number are always ODD. The only exception is 2, which is EVEN. Why did you pick 1995? Why not:1155=3x5x7x11, or 1365=3x5x7x13....and so on.
3*5*7*19=1995. The factors have 1, 3, 5, 7, and 9 in them (the first 5 odd numbers). Since you want to find the next lowest number with this property, you have two options. When you multiply two positive integers (say x and y), what you are doing is ((((x+y)/2)-((abs(y-x))/2))*(((x+y)/2)+((abs(y-x))/2))), or ((((x+y)/2)^2)-(abs(y/2-x/2))). So the farther apart x and y are, the lower answer you get (10*10=100, 11*9=99, 10+10=20, 11+9=20, abs(10-10)=0, abs(11-9)=2). So the options are 1*5*7*39, or 3*5*9*17. The first option is problematic because 1 isn't prime, so it would have to be 7*15*39. 3*5*9*17=2295, while 7*15*39=4095. If you try to improve on this, it eventually leads back to 3*5*9*17. So the answer is 2295.
For 4 integers (w, x, y, z), it is ((((w+x+y+z)/4)-((abs(z-y-x-w))/4))*(((w+x+y+z)/4)+((abs(z-y-x-w))/4))). I think (not 100% sure).
+118658 Guest 2, yours does not work because 9 is not a prime number.
The prime factorization of 1995, which is 3*5*7*19, uses each odd digit exactly one and 1995 is the smallest positive integer with this property. What is the next smallest?
Please show steps for solving.
1 and 9 are the only digits that is not prime so they have to be used in conjuction with digits
Mmm
maybe 3*5*7*91
No, 91 is not prime so that is not any good :(
So I want the smallest 3 digit number containing 9,1 and either 3,5,or 7
mabe 139*5*7
139 is prime :)
So I am going with 139*5*7 = 4865
