Question

How do you find all the factors of \[22\]?

Answer 1

Hint:In the given question, we have been given a natural number. We have to find the factors of the number. If a number can divide another number, then the first number is called a factor of the second number. And the second number is called a multiple of the first number. A prime number only has two factors – one and the number itself. While a composite number always has more than two factors. Two is the only even prime. So, if we have a number that is even but not two, then it is for sure composite.

Complete step by step answer:
The given number whose factors are to be found is \[22\].
We know, every number has at least two factors - \[1\] and the number itself.
So, two of the factors of the given number are \[1,22\].
We can easily solve it by using prime factorization,
\[\begin{array}{l}{\rm{ }}2\left| \!{\underline {\,
  {22} \,}} \right. \\11\left| \!{\underline {\,
  {11} \,}} \right. \\{\rm{ }}\left| \!{\underline {\,
  1 \,}} \right. \end{array}\]
Hence, \[22 = 2 \times 11\]
Thus, \[22\] has two more factors - \[2\] and \[11\].

So, \[22\] has four factors – \[1,2,11,22\].

Additional Information:
While the number of factors of a number is limited, i.e., at one point, the list of factors ends, or we can say, the list of factors is exhaustive. But, the number of multiples of a number is infinite. This is because the counting never ends, and by multiplying any number, we get one number more in the set of multiples.

Note: In the given question, we had to find the factors of \[22\]. At the first glance only, we can tell that the given number has more than two factors because it is not equal to two and is even. Then, we divide the number by two and find the rest of its factors; the set of factors will always contain one and the number itself.