Q.10 - Intermediate Algebra

Question

In the following exercises, find the prime factorization.

400

Step-by-Step Solution

Answer

The prime factorization of 400 is $2·2·2·2·5·5$

Step 1. Given information

The given number is 400.

The prime factorization of the given number is to be determined.

Step 2. Calculating the prime factors

For prime factorization, the given number is to be factored such that all the factors are prime numbers:

$$\begin{gathered} 400=2·200 \\ 400=2·2·100 \\ 400=2·2·2·50 \\ 400=2·2·2·2·25 \\ 400=2·2·2·2·5·5 \end{gathered}$$

The factors are all primes here and cannot be further factored.

Step 3. Conclusion

Therefore, the prime factorization of 400 is $2·2·2·2·5·5$