Achilles number
Imagine you have a toy box filled with many different toys. Your favorite toy is a car, but you also have some other toys like balls, blocks, and dolls. Your mom asks you to pick out all the toys that have wheels. You go through your toy box and find 4 toys: your car, a ball with a wheel inside, a block with a wheel on it, and a wagon. You put those 4 toys in a pile and show them to your mom.
Now, imagine if your toy box had all the numbers in it instead of toys. Your favorite number might be 10, but there are lots of other numbers in your box, like 1, 2, 3, 4, 5, 6, 7, 8, and 9. An Achilles number is a special kind of number that is like the toys with wheels - it has two factors (numbers that can be multiplied together to make it), and each factor has only one prime factor (a factor that is a prime number, which means it can't be divided by anything other than 1 and itself).
Let's use the number 72 as an example of an Achilles number. We can find its factors by listing all the numbers that divide evenly into it: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. We could also use prime factorization to find its factors - 72 = 2 x 2 x 2 x 3 x 3.
So now we know that 72 has two factors, 2 x 2 x 2 x 3 x 3, and each of those factors has only one prime factor: 2 and 3. That makes 72 an Achilles number!
It's like a special club for numbers that have these special qualities. Not all numbers can be in this club, but when a number can, we call it an Achilles number.
Now, imagine if your toy box had all the numbers in it instead of toys. Your favorite number might be 10, but there are lots of other numbers in your box, like 1, 2, 3, 4, 5, 6, 7, 8, and 9. An Achilles number is a special kind of number that is like the toys with wheels - it has two factors (numbers that can be multiplied together to make it), and each factor has only one prime factor (a factor that is a prime number, which means it can't be divided by anything other than 1 and itself).
Let's use the number 72 as an example of an Achilles number. We can find its factors by listing all the numbers that divide evenly into it: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. We could also use prime factorization to find its factors - 72 = 2 x 2 x 2 x 3 x 3.
So now we know that 72 has two factors, 2 x 2 x 2 x 3 x 3, and each of those factors has only one prime factor: 2 and 3. That makes 72 an Achilles number!
It's like a special club for numbers that have these special qualities. Not all numbers can be in this club, but when a number can, we call it an Achilles number.