Question

Express 3825 as a product of power of prime factors.

Answer 1

Hint: Here we will use the prime factorization method. In the prime factorization method, we will find the prime factors of the given number such that when we multiply the prime factors we will get the original number.

Complete step-by-step answer:
First, we will break 3825 into its factors. For 3825, the factor would be $3 \times 1275$ then again we will break 1275 into its factors, for 1275 this would be $2 \times 425$ and so on. We will continue this process until we get all the factors as a prime number.
Let’s do it step by step to understand it more clearly:-
$3825 = 3 \times 1275$
Now we will break 1275 into its factor.
$\Rightarrow$ $3825 = 3 \times 3 \times 425$
Again breaking 425 into its factors, we get
$\Rightarrow$ $3825 = 3 \times 3 \times 5 \times 85$
Again breaking 85 into its factors, we get
$\Rightarrow$ $3825 = 3 \times 3 \times 5 \times 5 \times 17$
We cannot break the factors further as all are prime factors.
Now, we can rewrite the expression as a product of the power of prime factors.
$3825 = {3^2} \times {5^2} \times {17^1}$.

Note: Prime factorization is a way of finding all the prime numbers that can be multiplied to get the original number. It is important to note that prime factorization means to have only a prime number as a factor and not a composite number. Prime numbers are the numbers that have only two factors and they are 1 and itself. On the other hand, composite numbers are the ones, which have more than 2 factors.
We might write ${3^2}$ and ${5^2}$ as 9 and 25 but this will be wrong, because we are asked to express 3825 as a product of power of prime factors. 9 and 25 are composite numbers and not prime numbers. We have to factorize it in order to get the correct prime factors.