Question

Find the prime factorization of 756

Short answer

The prime factorization of of 756 is$2^2\times 3^3\times 7^1$

Step-by-step solution

. Given information

Given the composite number is 756

To find out the prime factorization.

. Description of prime factorization

The prime factorization is the product of prime numbers is that equal number.

Find two factors whose product is the given number, and use these numbers to create two

branches.

If a factor is prime, that branch is complete.

If a factor is not prime, write it as the product of two factors and continue the process.

Write the composite number as the product of all the primes.

.  Prime factorization of the factors

Two factors of $756=27\times 28$

Factor of $27=3\times 3\times 3$,this is the prime factorization of 27.

Factor of$$\begin{gathered} 28=4\times 7 \\ =2\times 2\times 7 \end{gathered}$$

. Prime factorization of 756 

The factors of $27and28areprimefactors.$

So the prime factorization of$$\begin{gathered} 756=27\times 28 \\ =3\times 3\times 3\times 2\times 2\times 7 \\ =3^3\times 2^2\times 7^1 \end{gathered}$$