What is the prime factorization of 22

Asked by maham237 @ 07/01/2021 in Mathematics viewed by 253 People

A number is written with the following factorization: 22 x 3 x 54 x 8 x 112. Is this factorization
a prime factorization? Explain why or why not. If it is not correct, give the correct prime
factorization of the number.

Answered by maham237 @ 07/01/2021

This factorization is not a prime factorization. 22, 54, 8 and 112 are even numbers, so they are not prime (there is only one number that is even and prime - 2).

Correct prime factorization:

$22=2\cdot11\\\\3\, \text{ - prime number}\\\\54 = 9\cdot6=3\cdot3\cdot2\cdot3\\\\8=2\cdot2\cdot2\\\\112=56\cdot2=7\cdot8\cdot2=7\cdot2\cdot2\cdot2\cdot2$

so:

$22\cdot3\cdot54\cdot8\cdot112=2\cdot11\cdot3\cdot3\cdot3\cdot2\cdot3\cdot2\cdot2\cdot2\cdot7\cdot2\cdot2\cdot2\cdot2=\\\\=\boxed{2^9\cdot3^4\cdot7\cdot11}$

What is the prime factorization of 22

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