Question

What is the prime factorization of 63?

Answer 1

Hint: We are asked to find the prime factorization of a number. For that we need to repeatedly divide the number by the smallest prime possible and we need to that till it becomes 1. So, in short we need to find the prime numbers which when multiplied will give the number whose prime factorization is needed to be found out.

Complete step-by-step answer:
We need to find the prime factorization of a number, for which we will continuously divide the number by the smallest prime possible. For example, if the number is 6 then we first find the smallest prime that divides 6, which is 2 and then we divide it further by 3 because that is the smallest prime which divides 6 after 2. And now only 1 is left which means the prime factorization of 6 is as follows:
$6=2\times 3\times 1$
Now, we have 63. The smallest prime number that divides 63 is 3, so we have:
$63=3\times 21$
Now, we further factorize 21. The smallest prime number that divides 21 is 3 again, so till now we have reached:
$63=3\times 3\times 7$
Now, the number 7 does not decompose any further since it is the smallest prime that divides 7.
So the prime factorization of 63 has been obtained.

Note: You need to be very careful while giving the factors, because only prime factors are allowed while finding the prime factorization. For example, if you write $63=3\times 21$ then that would be wrong because 21 is not a prime number. So, you need to be aware while listing out the prime factors.