Use the unique factorization theorem to write the following integers in standard factored form. 2205

Daniaal Sanchez

Daniaal Sanchez

Answered question

2021-05-12

Use the unique factorization theorem to write the following integers in standard factored form.
2205

Answer & Explanation

Aamina Herring

Aamina Herring

Skilled2021-05-13Added 85 answers

Step 1
Unique Factorization Theorem.
For every integer n>1, there exists a positive integer k and distinct prime numbers
p1,p2,p3,....,pk and positive integers such that,
n=p1e1p2e2...pkek
Step 2
Perform prime factorization of the number.
2205 can be divided by 3.
2205=3×735
=3×3×245
=22×245
245 can be divided by 5.
2205=32×245
=32×5×49
49 can be divided by 7.
2205=32×5×49
=32×5×7×7
=32×5×72
Thus, the factorization of 2205 is 32×5×72

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