Greatest common factor of 14,28,and 42

Question

I don't really have any. 

Answer 1

Let's start with a definition; all great solutions in mathematics require a basic definition as well as some working knowledge about how numbers are related. The definition for greatest common factor is somewhat long and boring in any old math textbook. Instead let me give you my interpretation:

The greatest common factor of any two or more integers is the largest number that can evenly them without ending up with remainders. Sometimes it is helpful to list all of the known factors of the numbers in question in order to determine which factors they have in common. For the problem you've posted let us examine each list of factors carefully.

14: 1, 2, 7, 14

28: 1, 2, 4, 7, 14, 28

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

As we examine the lists it is pretty clear that they have common factors of 1, 2, 7, and 14. The greatest common factor asks for the largest of them, in this case 14. So the greatest common factor of 14, 28, and 42 is in fact 14.

Interesting Fact: Sometimes mathematicians like to use fancy notation to shorten this question. The notation for greatest common factor is gcf(x,y)=n where x and y are just some random integers and n is their greatest common factor. So for our question we could write gcf(14, 28, 42) = 14.

Answer 2

The factors of 14 (numbers that divide evenly into 14) are:   1, 2, 7, 14

The factors of 28 are:   1, 2, 4, 7, 14, 28

The factors of 42 are:   1, 2, 3, 6, 7, 14, 21, 42

 

The largest number that is Common (the GCF) to these lists is 14.

 

Another method is to list the prime factors:

14 has prime factors:   2 * 7

28 has prime factors:   2 * 2 * 7

42 has prime factors:   2 * 3 * 7

 

The prime factors 2*7 = 14 are Common to all three, so 14 is the GCF.

Answer 3

List the factors of each number.

 

14: 1, 2, 7, 14

28: 1, 2, 4, 7, 14, 28

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

 

The greatest factor these numbers have in common is 14.