Question

What is the prime factorization of \[35\]?

Answer 1

Hint : The process of expressing a given number as a product of prime factors is called a prime factorization. It is a process of factorizing a number in terms of prime numbers i.e the factors will be prime members.

Complete step-by-step solution:
The numbers that divide 35 exactly without leaving a remainder value are the factors of \[35\]. The factors of \[35\] can be positive or negative but it is not decimal. In mathematics, the numbers that divide \[35\]exactly are the factors of \[35\]. Thus the factors of \[35\]are \[1,5,7\]and \[35\]. Similarly, the negative factors of \[35\] are\[\left( { - 1} \right),\left( { - 5} \right),\left( 7 \right)\]and \[\left( { - 35} \right).\].
Positive factors of \[35{\text{ }} = {\text{ }}\left( {1 \times 35} \right),\left( {5 \times 7} \right)\]
Positive pairs of \[35 = \left( {1,35} \right),\left( {5,7} \right)\]
Factors of \[35\] by division method-
\[\dfrac{{35}}{1} = 35\] (Factor is \[1\] and remainder is \[0\])
\[\dfrac{{35}}{5} = 7\] (Factor is \[5\] and remainder is \[0\])
Therefore, prime factorization of \[35\] is.

Note:As we know, composite numbers have more than two factors, therefore this method is applicable only for composite numbers and not for prime numbers. For e.g.: prime factors of \[6\]will be \[2\]and \[3\] , the prime factors of \[26\]will be \[\;13\] and\[\;2\]etc.