Question

How do you write 525 as a product of its prime factors?

Answer 1

We know that Prime factors of a number are the set of prime numbers which when multiplied together give the actual number. This means that the prime factors divide the number completely. It is similar to factoring a number and considering only the prime numbers among the factors. So we will find the prime factors of a given number to determine the answer.

Complete step by step answer:
We are given the number 525.
We know that the smallest prime number is 2. But as the unit digit of 525 is not zero or an even number, it is not divisible by 2.
Therefore, we will now check the divisibility of 3 for the number 525.
The sum of all three digits of the given number is $5 + 2 + 5 = 12$ which can be divided by 3.
Thus, the given number is divisible by 3.
$\dfrac{{525}}{3} = 175$
$\Rightarrow 525 = 3 \times 175$
Now, we will check whether 175 is divisible by 3 or not.
The sum of digits of 175 is 13 which cannot be divided by 3. Thus, 175 is not divisible by 3.
Now, we will check the divisibility of the next prime number which is 5.
As the unit digit of 175 is 5, it is divided by 5.
$\dfrac{{175}}{5} = 35 \\\ \Rightarrow 175 = 35 \times 5 \\\$
Now, we can write our main number as
$\Rightarrow 525 = 3 \times 5 \times 35$
We know that 35 is also divisible by 5.
$
\dfrac{{35}}{5} = 7 \\

\Rightarrow 35 = 5 \times 7 \\
$$ \Rightarrow 525 = 3 \times 5 \times 5 \times 7$Here, we can see that all the factors are prime numbers. **Hence our final answer is:$525 = 3 \times 5 \times 5 \times 7$**

Note:
Here, we have applied the division method for finding the prime factors of the given number. The general steps for this method are: First step is, dividing the given number by the smallest prime number. In this case, the smallest prime number should divide the number exactly. Second step is, again dividing the quotient by the smallest prime number. Next step is, repeating the process, until the quotient becomes 1. Final step is to multiply all the prime factors.