Question

What are the prime factors of 230?

Answer 1

Hint: Prime factors are made up of two distinct words, prime and factor. Prime number is a number which has only two factors. Factors are numbers which have been multiplied to get the product. In other words, factors can divide the product perfectly with no reminder. We can find the prime factors of 230 by repeating the division method.

Complete step-by-step answer:
We need to find the prime factor of 230.
We can find the prime factor by repeated division. In this method we begin by dividing the number with its smallest prime number factor and we keep on dividing the resultant quotient with its smallest prime factor until we reach 1 as a final quotient.
Now take 230
Now we divide 230 by 2 then we will get 115 as a remainder.
  \[ \Rightarrow \dfrac{{230}}{2} = 115\] .
Again we divide 115 by 5 we will get 23 as a remainder.
 \[ \Rightarrow \dfrac{{115}}{5} = 23\] .
Again we divide 23 by 23 we will get 1 as a remainder.
 \[ \Rightarrow \dfrac{{23}}{{23}} = 1\] . We stop here.
Hence the prime factors of 230 are 2, 5 and 23.
So, the correct answer is “ 2, 5 and 23”.

Note: We generally use prime factors to find the highest common factor (HCF) and Lowest common multiple (LCM). We can also find the prime factor by factor tree method. That is we consider the given number as the base of the tree and we write down the pair of factors in the branches from of a tree. Again factorize the composite factors and write down the factor pairs in the branches from the tree. We repeat this until we find the prime factors of all composite factors.