Question

Find the prime factors of 12673.

Answer 1

Hint: We use the concept of prime factorization and write all prime factors of the given number and collect the powers of each prime factor using the law of exponents.
* Any number is said to be a prime number if it has no other factors other than 1 and the number itself.
* Prime factorization is a process of writing a number in multiple of its factors where all factors are prime numbers.
* Law of exponents states that when the base is same we can add the powers of that element i.e. \[{p^m} \times {p^n} = {p^{m + n}}\]

Step-By-Step answer:
We have to find the prime factors of the number 12673
We know prime factorization of a number is the representation of a number in terms of multiples of its prime factors.
\[ \Rightarrow 12673 = 19 \times 23 \times 29\]
Since no prime factor is repeated in the multiplication in RHS we cannot apply exponent rule as the prime factors are already in simplest form.
Since 19, 23 and 29 are prime numbers and are factors of the number 12673 we can write 19, 23 and 29 are prime factors of 12673.

\[\therefore \]Prime factors of 12673 are 19, 23 and 29.

Note: Many students make the mistake of writing the number 1 also as a prime factor but keep in mind 1 is neither prime nor composite, it is a factor but is not a prime factor of the number. We can write the number 1 and the number itself as the factors of the given number but they both are not prime numbers, so will not be prime factors as well.