Question

In which of the following expressions, prime factorization has been done:

(i) $24=2\times 3\times 4$
(ii) $56=7\times 2\times 2\times 2$
(iii) $70=2\times 5\times 7$
(iv) $54=2\times 3\times 9$

Answer 1

If a number can be expressed as product of the prime numbers then it is called Prime factorization.

(i) $24=2\times 3\times 4$

Which is not in Prime factorization. Since, $4$ is not a prime.

Prime factorization of $24$ is $24=2\times 2\times 2\times 3$

(ii) $56=7\times 2\times 2\times 2$

Which is in Prime factorization. Since, each factor is a prime.

(iii) $70=2\times 5\times 7$

Which is in Prime factorization. Since, each factor is a prime.

(iv) $54=2\times 3\times 9$

Which is not in Prime factorization. Since, $9$ is not a prime.

Prime factorization of $54$ is $24=2\times 3\times 3\times 3$

Hence in expressions (ii) and (iii), prime factorization has been done.