Find the prime factorization of 56.

Question
Polynomial factorization
asked 2020-10-20
Find the prime factorization of 56.

Answers (1)

2020-10-21
Step 1
Consider the number 56.
Since 56 is an even number, it is divisible by the prime number 2.
Note that, \(\displaystyle{56}={2}\times{28}\).
We proceed further by factorising composite factors after each step.
Next, we have to consider the factorisation of the composite factor 28 of 56.
Since 28 is an even number, it is divisible by the prime number 2.
Also, \(\displaystyle{28}={2}\times{14}\).
Substituting \(\displaystyle{28}={2}\times{14}\in{56}={2}\times{28},{w}{e}\ge{t}{56}={2}\times{2}\times{14}\).
Step 2
Next, we have to consider the factorisation of the composite factor 14 of 56.
Since 14 is an even number, it is divisible by the prime number 2.
Also, \(\displaystyle{14}={2}\times{7}\).
Substituting \(\displaystyle{14}={2}\times{7}\in{56}={2}\times{2}\times{14},{w}{e}\ge{t}{56}={2}\times{2}\times{2}\times{7}\).
Note that, all the factors in the right hand side of \(\displaystyle{56}={2}\times{2}\times{2}\times{7}\) are primes.
Hence, we stop here.
Note that, \(\displaystyle{56}={2}\times{2}\times{2}\times{7}={23}\times{7}\).
Thus,
\(\displaystyle{56}={2}\times{28}\)
\(\displaystyle={2}\times{2}\times{14}\)
\(\displaystyle={2}\times{2}\times{2}\times{7}\)
The prime factorisation of 56 is \(\displaystyle{2}\times{2}\times{2}\times{7}{\quad\text{or}\quad}{2}^{{3}}\times{7}\).
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