How do you find the gcf using lists of factors?

Answer 1

Example: 30 and 42

The factors of 30 are:

1, 2, 3, 5, 6, 10, 15, 30

The factors of 42 are:

1, 2, 3, 6, 7, 14, 21, 42

The common factors are:

1, 2, 3, 6

The Greatest Common Factor:

GCF = 6

Answer 2

1) The most primitive method: List several factors of each number. Check for common factors.This method is only appropriate for fairly small numbers.

2) Factoring, taking all common factors, and multiplying them.

This method is appropriate for medium-sized numbers - perhaps up to a 100, or 1000. In any case, for numbers that can easily be factored. (Factoring is tricky for large numbers.)

3) Euclid's algorithm quickly gives you the greatest common factor, without actually factoring any of the numbers.

This method is appropriate for numbers of any size.

Example: The greatest common factor of 14 and 10 is the same as the greatest common factor of 10 and 4 - where 4 is the remainder of the division, of 14 by 10.

Repeating this, gcf(10, 4) = gcf(4, 2)

gcf(4, 2) = gcf (2, 0)

Note that the greatest common factor of any number "n" and 0 is "n" (in this case, 2).

For more than two numbers, for example, gcf(a, b, c) gcf((gcf(a, b), c). In other words, take the greatest common factor of the first two numbers, then the greatest common factor of that result with the third number, etc.

Answer 3

The number 1 will always be a common factor of any pair of numbers. If the other factors of two different numbers are all different, then the greatest common factor is the number 1.

Answer 4

Factor tree

Listing the factors