Ever found yourself looking at two numbers and wondering what they have in common? It's a bit like meeting two new people and trying to figure out what connects them, isn't it? Today, we're going to do just that with the numbers 14 and 21.
Think of numbers as having a set of 'friends' – these are their factors. Factors are simply the numbers that can divide another number perfectly, with no remainder left over. It's like finding all the pairs of building blocks that can be multiplied together to create a specific number.
So, let's find the 'friends' of 14 first. We can start by thinking about multiplication. What pairs of numbers multiply to give us 14? Well, there's 1 multiplied by 14, which gives us 14. And then there's 2 multiplied by 7, which also equals 14. So, the factors of 14 are 1, 2, 7, and 14.
Now, let's turn our attention to 21. What pairs of numbers multiply to make 21? We know that 1 times 21 equals 21. And if we think a little further, 3 times 7 also gives us 21. So, the factors of 21 are 1, 3, 7, and 21.
We've found the individual 'friend groups' for both 14 and 21. The next step, and the really interesting part, is to see which friends they share. Looking at our lists – factors of 14 are {1, 2, 7, 14} and factors of 21 are {1, 3, 7, 21} – we can spot the numbers that appear in both lists.
Do you see them? Yes, the number 1 is a factor of both 14 and 21. And the number 7 is also a factor of both 14 and 21. These are what we call the 'common factors' – the numbers that are friends with both 14 and 21.
So, the common factors of 14 and 21 are 1 and 7. It's a simple concept, but understanding it is a key step in many areas of mathematics, like finding the greatest common factor (GCF) or working with fractions. It's all about finding that shared ground between numbers.
