What is Common Factors?

S3-SA4-0028

Grade Level:

Class 6

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

Definition

What is it?

Common factors are numbers that divide two or more given numbers exactly, without leaving any remainder. Think of them as shared 'divisors' between different numbers.

Simple Example

Quick Example

Imagine you have two teams for a cricket match. Team A has 12 players and Team B has 18 players. If you want to divide both teams into smaller groups of equal size, the possible group sizes that work for both teams are the common factors of 12 and 18.

Worked Example

Step-by-Step

Let's find the common factors of 10 and 15.

Step 1: Find all the factors of 10.
Factors of 10 are: 1, 2, 5, 10 (because 1x10=10, 2x5=10).

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Step 2: Find all the factors of 15.
Factors of 15 are: 1, 3, 5, 15 (because 1x15=15, 3x5=15).

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Step 3: Look for the numbers that appear in BOTH lists of factors.
Factors of 10: {1, 2, 5, 10}
Factors of 15: {1, 3, 5, 15}

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Step 4: The numbers common to both lists are 1 and 5.

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Answer: The common factors of 10 and 15 are 1 and 5.

Why It Matters

Understanding common factors helps in many areas, from simplifying fractions in math to organizing data in computer science. Engineers use it to find optimal designs, and even in cryptography, it plays a role in securing information. It's a foundational skill for future careers in AI, data science, and engineering.

Common Mistakes

MISTAKE: Listing only the prime factors as common factors. | CORRECTION: Remember to include 1 and any composite factors that are common.

MISTAKE: Forgetting to list ALL factors of each number before comparing. | CORRECTION: Always find every single factor for each number first to avoid missing any common ones.

MISTAKE: Confusing common factors with common multiples. | CORRECTION: Factors divide a number, multiples are what a number is multiplied by. They are opposite concepts.

Practice Questions

Try It Yourself

QUESTION: What are the common factors of 6 and 9? | ANSWER: 1, 3

QUESTION: Find all the common factors of 12 and 20. | ANSWER: 1, 2, 4

QUESTION: A shopkeeper has 24 apples and 36 oranges. He wants to pack them into baskets, with each basket having the same number of apples and the same number of oranges. What are the possible numbers of fruits he can put in each basket (representing common factors)? | ANSWER: 1, 2, 3, 4, 6, 12

MCQ

Quick Quiz

Which of the following is NOT a common factor of 16 and 24?

The Correct Answer Is:

The factors of 16 are 1, 2, 4, 8, 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The common factors are 1, 2, 4, 8. Therefore, 6 is not a common factor.

Real World Connection

In the Real World

When you are simplifying fractions, like reducing 10/15 to 2/3, you are using common factors. You divide both the numerator and denominator by their common factor (which is 5 in this case). This skill is also used in computer programming to optimize code and make calculations more efficient.

Key Vocabulary

Key Terms

FACTOR: A number that divides another number exactly, leaving no remainder. | DIVISOR: Another name for a factor. | COMMON: Shared by two or more things. | REMAINDER: The amount left over after a division.

What's Next

What to Learn Next

Great job understanding common factors! Next, you should learn about the 'Highest Common Factor' (HCF) or 'Greatest Common Divisor' (GCD). It builds on this concept by asking you to find the largest number among all the common factors.