Question

What are the prime factors of \[102\]?

Answer 1

Hint: We are given a question asking us to find the prime factors of \[102\]. Prime numbers are those numbers which have their factors as 1 and the number itself. So, prime factors of \[102\] would mean to express the number \[102\] as the product of prime numbers. We will simply divide the given number \[102\] by the smallest prime number which can divide the number and we will continue this process until all the factors are prime numbers only. Hence, we will have the prime factors of \[102\].

Complete step by step answer:
According to the given question, we are given a number \[102\] and we are asked to find the prime factors of the given number.
A prime number corresponds to those numbers which has 1 and the number itself as the factors. When we are asked to find the prime factor of a number, it means we have to express the given number as the product of prime numbers alone.
We simply have to divide the given number by the smallest prime number which can divide the given number and we will continue this process until all the factors of the given number are only prime numbers.
The number we have is,
\[102\]
It is an even number, so we can divide it by 2 and so we get,
\[102=2\times 51\]
We can see that the factors of the number 102 has 51 too, which is not prime and so we will divide it further by another prime number, which is, 3, and so we get,
\[102=2\times 3\times 17\]
Here, 2, 3 and 17 are all prime numbers.
Therefore, the prime factors of \[102=2\times 3\times 17\].

Note: The above method that applied in order to find the prime factors of the given number is prime factorization. Like mentioned above, it requires the factors of any number to be written only in terms of prime factors alone. And also make sure that the division is done correctly.