x5y2 - 2 = 0 ... makes sense
You look at the exponents. x5y2 and x3y4 The greatest common factor of these is the largest exponent of each. So the greatest common factor is: x3y2
Look at the numbers (coefficients) in the problem. Use your knowledge of multiplication / division to think of the largest common factor of these coefficients, in other words, the largest number that divides into all of them.Assuming one variable is common to all the individual terms, find the smallest exponent. That will be the variable part of the GCF.Alternate method. This is probable what your book and teacher will tell you to do when you are first learning to do this.Do a prime factorization of each term. Look for common factors in EVERY term. All these common factors become part of the GCF and are moved to the front of the parenthesis. All other factors are left inside the parenthesis. Simplify both outside and inside the parenthesis by multiplying and using exponents for variables.Ex: 30 x5y2 + 45x3y4= 2 . 3 . 5 . x . x . x . x . x . y . y + 3 . 3 . 5 . x . x . x . y . y . y . ylook for common factors 3,5,x,x,x,y,y