Question

what is the procedure for finding common factors of 2 numbers. ie how do you find the common factor of 125 and 350.

Answer 1

A method that will always work is to find the prime factors of each number and then collect the common ones. Here is an example.
125
5*25
5*(5*5)
So, the prime factors of 125 are 5,5,5

Do the same for 350.
350
5*70
5*(7*10)
5*7*(2*5)
5*7*2*5
So, the primer factors of 350 are 7,5,5,2.

Now, find all the common factors. 125 has three fives and 350 has two fives. The other numbers are not in both 125 and 350. Taking the two fives wqhich are in each, the greatest common factor is 5*5 or twenty-five.

Here is another example without repeated factors. Find the greatest common factor of 35 and 30.

35
5*7

30
5*6
5*(2*3)
5*2*3

the only number that both 35 and 30 share is 5, so 5 is the greatest common factor.

Answer 2

http://math.about.com/library/bldivide.htm

\[\text{Divisors}[125]\to \{1,5,25,125\} \]\[\text{Divisors}[350]\to \{1,2,5,7,10,14,25,35,50,70,175,350\} \]

Answer 3

Thank you. Got it now.