Question

find the canonical decomposition of 2013​

Answer 1

SOLUTION

TO DETERMINE

The canonical decomposition of 2013

CONCEPT TO BE IMPLEMENTED

1. Every integer n > 1 can be expressed uniquely as a product of prime powers

2. If n is an integer. Then n can be written as

$\sf{n = {p_1 }^{a_1} \times {p_2 }^{a_2} \times ... \times {p_n }^{a_n} }$

Where

$\sf{p_1 < p_2 < ... < p_n} \: \: and$

$\sf{a_1, a_2,..., a_n \in \mathbb{N}}$

EVALUATION

Here the given number is 2013

Now

$2013 = 3 \times 11 \times 61$

$\therefore \: \: 2013 = {(3)}^{1} \times {(11)}^{1} \times {(61)}^{1}$

Which is the required canonical decomposition of 2013

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