Question

What is the prime factorization of \[125\] ?

Answer 1

Hint: To find the answer to the question given above, divide \[125\] by just prime numbers to find the prime factorization. Prime numbers are whole numbers greater than \[1\] that can only be divided equally by themselves and \[1\]. Also, remember a composite number is a real number greater than \[1\] that is not prime.

Complete step-by-step answer:
We have to find prime factorization of \[125\].
Now, we know Factorization, also known as factoring, is the process of writing a number or another mathematical entity as a result of many variables, which are usually smaller or simpler objects of the same nature.
We have to find the answer through prime factorization.
Since, \[125\] ends with \[5\], it is divisible by \[5\] and we know that \[5\] is a prime number.
So, \[125 \div 5 = 25\]
Now, \[25\]has to be factored into its prime factors.
We get:
\[25 = 5 \times 5\]
Hence, the prime factorization of \[125\] is:
\[125 = 5 \times 5 \times 5\].
This can be written as: \[125 = {5^3}\].
So, the final answer is: \[{5^3}\].

Note: While solving questions similar to the one given above, remember that prime factorization is the method of factoring a number in terms of prime numbers, with prime numbers as the variables. The method of identifying prime numbers and multiplying them together to get the original number is known as prime factorization. The prime factors of \[16\] are, for example, \[2{\text{ 2 2 2}}\]. It's also possible to write this as\[{\text{ 24}}\]. The division method and the factor tree method are two methods for determining a number's prime factors.