Question

What is the prime factorization of \[86\]?

Answer 1

Hint: In this question, we need to find the prime factors of the given number \[86\] by using the prime factorization method. Prime factorization is nothing but a method of finding factors of a number in terms of prime numbers. First, we need to divide the given number by the least prime number. Then we need to divide the result by either the same prime number or the next prime number and then we need to follow the same process until we get the quotient as a prime number. Finally, we need to multiply all the prime factors of the given number to get the required answer.

Complete step-by-step solution:
Given , \[86\]
Here we need to find the prime factors by using the prime factorization method.
On observing the given number, \[86\] is a composite even number. We can divide the given number by the least prime number. The least prime number is \[2\].
On dividing by \[2\] ,
We get,
\[\Rightarrow 86\div 2\]
On simplifying,
We get,
\[\Rightarrow 43\]
On observing the number \[43\], \[43\] is the prime number. As we got the quotient \[43\] as a prime number, we don’t need to divide the number further.
Thus the prime factorization of \[86\] is \[2,43\] . So we can also write it as \[86=2\times43\] .

The prime factorization of \[86\] is \[2\times43\] .

Note: We need to know that each number is a factor of itself and the number \[1\] is a factor of every number, the number \[1\] can be neglected. The product of the factors should be the number itself and thus, the numbers become the prime factors. Mathematically, the composite number has to be factorized by a prime factor and a composite factor and this has to be continued until all the factors become the prime factors.