Question

What is the prime factorization of 2025?

Answer 1

Hint: Prime factorization means expressing a number as a product of prime numbers only. Every number is a prime number in prime factorization. For example: Prime factors of 10 are 2 and 5.
We have discussed the method of prime factorization to find the factors of 2025 in detail below.

Complete step-by-step answer:
In this question, we are given a number and we have to find its factors using the prime factorization.
First of all, let us understand what factors are and then prime factorization methods to find the factors of a given number.
Multiplying two numbers gives a product and these two numbers are called factors. A factor completely divides a number and leaves remainder 0. For example: factors of 15 are 1, 3, 5 and 15.
Now, prime factorization means expressing a number as a product of prime numbers only. Every number is a prime number in prime factorization.
Now, let us prime factorize the given number 2025.
$ \Rightarrow $Prime factors of 2025$ = 5 \times 405$
                                             $
   = 5 \times 5 \times 81 \\
   = 5 \times 5 \times 9 \times 9 \\
   = 5 \times 5 \times 3 \times 3 \times 3 \times 3 \\
 $
Hence, we can write 2025 as
$ \Rightarrow 2025 = {5^2} \times {3^4}$
Hence, the prime factors of 2025 are 3 and 5.

Note: Factors are always integers or whole numbers, it can never be fraction or decimal.
All even numbers have a common factor that is 2.
All the numbers ending with 5 have a common factor that is 5.
All the numbers ending with 0 have common factors 2, 5 and 10.