Euler Project problem #3

You are doing an unnecessary division every time the loop cycles:

    while x<(a/x):

To avoid this, you can define a third variable and only set it when a changes.

a may be a perfect square, as Peter Taylor mentioned. To return the correct answer in this case, use:

    while x <= (a/x):

You are comparing a changing value to another changing value. 'x' goes up while 'a/x' comes down to meet it. This works fine, but makes it hard to estimate how long the loop will run for.

    x < (a / x)

Is equivalent to:

    x < sqrt(a)

This makes it clear that, if a % x never equals 0, the loop will continue to run until x reaches \$\sqrt{a}\$. This happens for prime input, e.g. a = 600851475149.

PEP8 recommends surrounding binary operators (=, ==, +=, etc.) with a single space on either side. For directional operators (*, /, -, +, %), spaces are used to make the order of operations clear (for example, a*b + c*d). In your case, there is no order of operations to worry about, so you can leave the spacing around / and % as it is.

Adding the improvements suggested by Peter Taylor and Graipher results in:

from math import sqrt

a = 600851475143
sqrt_a = sqrt(a)
x = 2
while x <= sqrt_a:
    if a%x == 0:
        a = a/x
        sqrt_a = sqrt(a)
    else:
        x+=1
print a

Which is immediately recognizable as a correct implementation of trial division. It's mathematically equivalent to yours (except the edge case of squares Peter Taylor spotted), so, great job!