Find the prime factorization of 56.

Question

berggansS · Accepted Answer

Step 1
Consider the number 56.
Since 56 is an even number, it is divisible by the prime number 2.
Note that,

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,

28 = 2 \times 14

.
Substituting

28 = 2 \times 14 \in 56 = 2 \times 28, w e \geq 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,

14 = 2 \times 7

.
Substituting

14 = 2 \times 7 \in 56 = 2 \times 2 \times 14, w e \geq t 56 = 2 \times 2 \times 2 \times 7

.
Note that, all the factors in the right hand side of

56 = 2 \times 2 \times 2 \times 7

are primes.
Hence, we stop here.
Note that,

56 = 2 \times 2 \times 2 \times 7 = 23 \times 7

.
Thus,

56 = 2 \times 28

= 2 \times 2 \times 14

= 2 \times 2 \times 2 \times 7

The prime factorisation of 56 is

2 \times 2 \times 2 \times 7 or 2^{3} \times 7

.

Find the prime factorization of 56.

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