Question

The process of finding the factors of a given number (or expression) is called
(a) Multiplication
(b) Factorisation
(c) Division
(d) Addition

Answer 1

Hint: Here, we need to find which of the given options can fill the blank. We will check the definitions of multiplication, factorisation, division, and addition with examples to find which of the options is the correct answer.

Complete step-by-step answer:
We will check the definitions of the given terms to find which of the options is correct.
Multiplication is the repeated addition of equal groups. It helps in adding multiple equal groups quickly. It is denoted by the symbol $$\times$$. Brackets may also be used to denote multiplication.
For example: Suppose that the number 2 is added repeatedly 15 times, that is $$2+2+\dots \dots +2$$ 15 times. This can be represented using multiplication as $$2\times 15=30$$.
Therefore, multiplication is not the process of finding the factors of a given number or expression.
Thus, option (a) is not the correct answer.
Factorisation is the process of taking out common factors from the terms in an expression, and rewriting the expression using a parentheses. It can be used to simplify various calculations.
For example: To calculate $$154+385$$, we can factorise the common factor, 77, from the expression.
Thus, the expression becomes
$$154+385=77\left(2+5\right)$$
We have factored the expression, making it easier to solve by adding the terms in the parentheses, that is $$2+5=7$$, and then multiplying 77 by 7.
We can also factorise expressions with variables.
For example: $$400x^2{y}^{2}z+200x{y}^{2}z$$ can be written as $$200x{y}^{2}z\left(2x+1\right)$$ by factoring out the common factor $$200x{y}^{2}z$$.
Therefore, the process of finding the factors of a given number (or expression) is called factorisation.
Thus, the correct option is option (b).

Note: We do not need to check the definitions of division or addition since the given question has only one correct answer, which we have obtained. Division is the process of distributing a number of things in a certain number of equal parts. Addition is the process of finding the sum of two or more numbers.