SOLUTION: How many ordered triples (X,Y,Z) of postive intgers satisfy X*Y*Z=4000?
Algebra.Com
Question 30470: How many ordered triples (X,Y,Z) of postive intgers satisfy X*Y*Z=4000?
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
X*Y*Z=4000 = 4*(2*5)^3 = 2^5* 5^3.
so X, Y, Z are in the form 2^i * 5^j (X= 2^i1 * 5^j1,..
with i1+i2+i3 = 5 and j1+j2+j3 = 3.
there are C(3+5-1, 5) = C(7,5) = 21 possible i's(why?)
and C(3+3-1, 3) = C(5,3) = 10 possible j's
Totally, there are 21*10 = 21 possible ordered triples (X,Y,Z).
Try X*Y = 2^3* 5^2
Kenny
RELATED QUESTIONS
How many ordered triples (x,y,z)) satisfy x^2 + y^2 +z^2 < 4 where x,y,z are integers
(answered by Alan3354)
Find the number of ordered triples (x,y,z) of real numbers that satisfy
{{{x + y - z = (answered by my_user_id)
What are all ordered triples of numbers (x, y, z) which satisfy the system of equations
(answered by KMST)
solve ordered triples
x+y+z=7
x-7+2z=7... (answered by richwmiller)
Let S be a set with eleven elements. How many 4 element subsets does S have? How many... (answered by ikleyn)
How many ordered pairs (x,y) of
integers satisfy…... (answered by Nate)
How many ordered pairs of integers (x, y) satisfy y^2 - xy + x =... (answered by Edwin McCravy)
How many ordered pairs of positive integers (x,y) satisfy the equation {{{... (answered by ankor@dixie-net.com,ikleyn)
How many ordered pairs of positive integers (x,y) satisfy the equation x= 4-x divided by... (answered by ikleyn)