Use the unique factorization theorem to write the following integers in standard factored form. 4116

fortdefruitI

fortdefruitI

Answered question

2021-05-21

Use the unique factorization theorem to write the following integers in standard factored form.
4116

Answer & Explanation

izboknil3

izboknil3

Skilled2021-05-22Added 99 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.
4,116 can be divided by 2.
4116=2×2058
2058 can also be divided by 2.
4116=2×2058
=2×2×1029
=22×1029
1029 can be divided by 3.
4116=22×1029
=22×3×343
343 can be divided by 7.
4116=22×1029
=22×3×7×49
Again divide 49 by 7.
4116=22×3×7×49
=22×3×7×7×7
=22×3×73
Thus, the factorization of 4116 is 22×3×73.

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