Question

What are the factors of 34?

Answer 1

Hint: First understand the meaning of the term ‘factor’ of a number. Now, to find the factors of 34 write it as the product of its primes. Group the factors and check how many different factors (prime or composite) can be formed. Also, use the fact that 1 is a factor of every number and a number is a factor of itself to add two more factors in the list.

Complete step by step solution:
Here we have been provided with the number 34 and we are asked to find its factors. First we need to understand the term ‘factor’.
Now the term ‘factor’ (x) of a number (y) means x divides y completely without leaving any remainder. For example: 56 can be divided by 2, 4, 7, 8, 14 and 28 without leaving any remainder, so they are the factors of 56. Also you may know that 1 is a factor of every number and a number is a factor of itself so we can say 1 and 56 are also the factors of 56.
Let us come to the question. We have to write the factors of 34, so writing it as the product of its primes we get,
$\Rightarrow 34=2\times 17$
Clearly we can see that 2 and 17 are the factors of 34. Also, we have 1 and 34 as its factors.
Hence, the factors of 34 are: - 1, 2, 17 and 34.

Note: Note that here we do not have to find the prime factors only but we have to find all the factors whether prime or composite. To find the composite factors we need to group different prime factors, so the basic requirement is that you must know how to write a number as the product of its prime so that we can form the groups easily.