Question

How do you write the prime factorization of 110?

Answer 1

Hint: As we can see that the word “prime factor” is made up of two distinct terms. Prime and factor. When we multiply two numbers, we get the product. Factors are the numbers which have been multiplied to get the product. In that factor we only choose the prime number. Prime number is a number which only has two factors ‘1’ and the number itself.

Complete step-by-step answer:
Given that we need to find the prime factor of 110.
We solve this using the repeated division method,
If we divide 110 by 2 we get 55 as remainder. We know that 55 is not divided by 3 and 4. So 55 is divided by 5 we get 11 as a remainder. 11 is a prime number hence it is divided by 11 only.
That is we have factors of 110 are 2, 5 and 11
\[ \Rightarrow 110 = 2 \times 5 \times 11\].
We can see that all the factors are prime numbers.
Hence the prime factors of 110 are 2, 5 and 11.
So, the correct answer is “2, 5 and 11”.

Note: We know that 2 is a prime number because the factors of 2 are 1 and the number itself (2). Follow the same procedure for these kinds of problems. In the above we used a repeated division method. As the name suggests in this method we begin by dividing the number with its smallest prime factor until we reach 1 as the final quotient. This is what we did in the above problem.