Question

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

Polynomial factorization
ANSWERED
asked 2021-06-02
Use the unique factorization theorem to write the following integers in standard factored form.
5733

Answers (1)

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 \(3x^{2}\times 7^{2}\times 13\).
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