Chapter 5.1, Problem 30WE

To determine

To find: The prime factorization of given number.

Answer to Problem 30WE

The prime factorization of 120 is $120=2\times 2\times 2\times 3\times 5=2^3\times 3\times 5$ .

Explanation of Solution

Given information:

The given number is 120.

Formula used:

The factors of an integer z are the prime numbers $p_1,p_2,p_3\dots$ , such that $z=p_1\times p_2\times p_3\times \dots \times p_n$ . The expression $z=p_1\times p_2\times p_3\times \dots \times p_n$ is called the prime factorization of integer z.

Calculations:

The given number is 120.

In factor form the integer 120 can be written as

  $120=2\times 2\times 2\times 3\times 5$

The numbers 2, 3 and 5are prime numbers.

Hence, the prime factors of integer120 are 2, 2, 2 3, and 5. Therefore, the prime factorization of 120 is $120=2\times 2\times 2\times 3\times 5=2^3\times 3\times 5$ .

Conclusion:

The prime factorization of 120 is $120=2\times 2\times 2\times 3\times 5=2^3\times 3\times 5$ .