What is Common Factor Method? | Simple Explanation for Class 6

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What is Common Factor Method of Factorisation?

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Common Factor Method of Factorisation is a way to rewrite an expression as a product of its factors. We look for a number or a variable that is common to all terms in the expression and 'take it out' as a common factor. This simplifies the expression by showing what terms multiply together to form the original expression.

Simple Example

Quick Example

Imagine you have two friends, Rohan and Priya, buying samosas. Rohan buys 3 samosas and Priya buys 5 samosas. If each samosa costs the same, say 'S' rupees, then Rohan spends 3S and Priya spends 5S. The total money spent is 3S + 5S. Using the common factor method, we can say they collectively spent S * (3 + 5) = 8S rupees. Here, 'S' is the common factor.

Worked Example

Step-by-Step

Let's factorise the expression: 4x + 12

Step 1: Identify the terms in the expression. The terms are 4x and 12.
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Step 2: Find the factors of each term.
Factors of 4x are 1, 2, 4, x, 2x, 4x.
Factors of 12 are 1, 2, 3, 4, 6, 12.
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Step 3: Find the greatest common factor (GCF) among the numerical parts (4 and 12). The GCF of 4 and 12 is 4.
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Step 4: Check if there's a common variable. In 4x + 12, 'x' is only in the first term, so there is no common variable.
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Step 5: The greatest common factor for the entire expression is 4.
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Step 6: Rewrite each term by dividing it by the common factor (4).
4x divided by 4 is x.
12 divided by 4 is 3.
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Step 7: Write the common factor outside a bracket, and the results of the division inside the bracket. So, 4x + 12 = 4(x + 3).

Answer: The factorised form of 4x + 12 is 4(x + 3).

Why It Matters

Understanding factorisation helps you simplify complex problems, just like simplifying a long cricket score. In Computer Science, it's used in algorithms to make programs faster. Even in Data Science, factorisation helps organise large datasets, which can lead to better predictions, like forecasting monsoon rainfall.

Common Mistakes

MISTAKE: Not finding the GREATEST common factor (GCF). For example, factorising 6x + 9 as 3(2x + 3), but leaving 6x + 9 as 1(6x + 9) or 3(2x+3) and thinking 3 is not the GCF. | CORRECTION: Always look for the largest number and highest power of variables that divide all terms. The GCF of 6x and 9 is 3.

MISTAKE: Forgetting to include a term inside the bracket after dividing by the common factor. For example, factorising 5y + 5 as 5(y). | CORRECTION: Remember that when you divide 5 by 5, the result is 1. So, 5y + 5 should be 5(y + 1).

MISTAKE: Not checking your answer by multiplying the factors back. For example, thinking 2(x + 3) is the factorisation of 2x + 5. | CORRECTION: Always multiply the common factor back into the bracket to see if you get the original expression. 2(x + 3) = 2x + 6, not 2x + 5. So, 2x + 5 cannot be factorised by the common factor method.

Practice Questions

Try It Yourself

QUESTION: Factorise 7a + 14. | ANSWER: 7(a + 2)

QUESTION: Factorise 10m - 25n. | ANSWER: 5(2m - 5n)

QUESTION: Factorise 9p + 18q + 27r. | ANSWER: 9(p + 2q + 3r)

MCQ

Quick Quiz

Which of the following is the correct factorisation of 8x + 16?

2(4x + 8)

4(2x + 4)

8(x + 2)

8x + 16

The Correct Answer Is:

The greatest common factor of 8x and 16 is 8. So, dividing each term by 8 gives x and 2 respectively, making the factorised form 8(x + 2). Options A and B use common factors, but not the greatest one.

Real World Connection

In the Real World

Imagine a factory making mobile phone covers. They produce 'N' covers for Samsung phones and 'M' covers for Redmi phones. If each cover requires 'C' units of plastic, the total plastic needed is NC + MC. Using factorisation, this becomes C(N + M). This helps the factory manager quickly calculate total plastic needed based on the total number of covers, no matter the brand, simplifying inventory management.

Key Vocabulary

Key Terms

FACTOR: A number or expression that divides another number or expression exactly | TERM: A single number, variable, or a product of numbers and variables in an expression | COMMON FACTOR: A factor that is shared by two or more numbers or terms | GREATEST COMMON FACTOR (GCF): The largest common factor of two or more numbers or terms | EXPRESSION: A combination of numbers, variables, and operation symbols (+, -, *, /) but without an equals sign

What's Next

What to Learn Next

Great job understanding common factors! Next, you can explore 'Factorisation by Grouping'. This method builds on common factors by applying it to expressions with four or more terms, opening up more complex problem-solving techniques.