Question

How do you write the factor tree for $120$?

Answer 1

Hint: First we will reduce the equation further if possible. Then we will try to factorise the terms in the equation. Split the middle term and factorise the equation. Then equate the factors equal to zero and evaluate the value of the variable.

Complete step by step solution:
Factors of $120$ refers to all the different combinations of the two factors of $120$ which you will multiply together to get the final answer as $120$.
Now this is a two step process. First, we start by creating a list of all the factors of $120$. Then next we will pair all the different combinations of these factors and it will finally give us all the factor pairs of $120$.
So, the factors of $120$ are:
$120 = 1,2,3,4,6,8,12,15,20,24,30,60,120$
Now if we make different combinations and hen make the tree like structure, it looks like this,
$
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,120 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,/\,\,\,\,\backslash \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,60\,\,\,\,\,2 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,/\,\,\,\,\,\backslash \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,30\,\,\,\,\,\,\,2 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,/\,\,\,\,\,\backslash \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,15\,\,\,\,\,\,\,\,\,2 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,/\,\,\,\,\,\backslash \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,5\,\,\,\,\,\,\,\,3 \\
 $

Note: Factorisation consists of writing a number or another mathematical objects as a product of several objects of the same kind. In particular, a univariate polynomial with complex coefficients admits a unique factorisation into linear polynomials; this is a version of the fundamental theorem of algebra.by the fundamental theorem of arithmetic, every integer greater than $1$ has unique factorisation into prime numbers, which are those integers which cannot be further factored into the product of integers greater than one.