Factorization — taking out common factors

Factorization is defined as the process of rewriting an expression as a product of its factors. It is the reverse of expanding brackets.

Expanding means multiplying out brackets, for example $2(x+4)=2x+8$. Factorizing goes the other direction: $2x+8=2(x+4)$, which is a product of $2$ and $(x+4)$.

The correct answer is 'Rewriting an expression as a product of its factors' because that is exactly what factorization does.

The question asks for the correct description of factorization. We need to pick the option that matches its definition.

Multiplying out brackets describes expanding, not factorizing. For example, $3(x+2)=3x+6$ is expansion. This option is eliminated.

'Adding like terms' describes simplifying or collecting like terms, a different algebraic skill. This is not factorization.

Finding the value of a variable describes solving an equation, which is a separate process from factorization.

The remaining option — 'Rewriting an expression as a product of its factors' — correctly describes factorization.

Factors of 18: $1,2,3,6,9,18$. Factors of 24: $1,2,3,4,6,8,12,24$.

The factors that appear in both lists are: $1,2,3,6$.

The largest factor shared by both numbers is $6$, so $\text{HCF}(18,24)=6$.

We need the largest number that divides evenly into both $18$ and $24$.

$9$ divides $18$ evenly ($18÷9=2$), but $24÷9=2.67$, which is not a whole number. So $9$ is not a common factor.

$4$ divides $24$ evenly ($24÷4=6$), but $18÷4=4.5$, which is not a whole number. So $4$ is not a common factor.

$3$ divides both $18$ ($18÷3=6$) and $24$ ($24÷3=8$), so it is a common factor. However, $6$ is larger and also divides both numbers, so $3$ is not the highest common factor.

$6$ divides $18$ ($18÷6=3$) and $24$ ($24÷6=4$) evenly, and no larger number does. So $\text{HCF}(18,24)=6$.