# Use the unique factorization theorem to write the following integers in standard factored form. 5733

Polynomial factorization
Use the unique factorization theorem to write the following integers in standard factored form.
5733

2021-06-03
Step 1
According to unique factorisation theorem every number can be represented in the form of positive prime number with exponents.
Various prime numbers are 2,3,5,7,9,11,..
Step 2
Divide the number with prime number, starting from least to determine whether it is a factor or not.
$$5733 = 3\times 1911$$
$$=3^{2}\times 637$$
$$=3^{2}\times 7 \times 91$$
$$=3^{2}\times 7^{2}\times 13$$
So, prime factorization of 5733 is $$3x^{2}\times 7^{2}\times 13$$.