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Suppose you have a fraction in the form a/b and suppose c is a common factor of a and b.

c is a factor of a so that a = c*x

c is a factor of b so that b = c*y

where x and y are integers.

And so a/b = cx/cy = x/y.

The process is as follows:

  1. find a common factor, c, of the numerator (a) and the denominator (b).
  2. the new numerator is the old numerator divided by the common factor that is, x = a/c;
  3. the new denominator is the old denominator divided by the common factor that is, y = b/c;
  4. the new fraction is x/y.
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Look for common factors in the two numbers. Divide both numbers by the common factors. Continue until there are no more common factors.


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The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder. Factors go into numbers, numbers go into multiples.


What is the greatest common factor of 36 and 90?

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Related questions

How do you change a fraction into simplest form?

You check whether numerator and denominator (top and bottom) of the fraction have common factors. Then you divide both by the common factors. Continue, until there are no more common factors.


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Look for common factors in the two numbers. Divide both numbers by the common factors. Continue until there are no more common factors.


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