What is a Factor Pair?

S1-SA1-0128

Grade Level:

Class 4

Maths, Computing, Number Theory

Definition

What is it?

A factor pair for a number is a set of two numbers that, when multiplied together, give you that original number. Think of them as partners who work together to make a specific number.

Simple Example

Quick Example

Imagine you have 12 ladoos. You want to arrange them in equal rows. If you put 2 ladoos in each row, you will have 6 rows (2 x 6 = 12). So, (2, 6) is a factor pair for 12. Similarly, if you put 3 ladoos in each row, you will have 4 rows (3 x 4 = 12), making (3, 4) another factor pair.

Worked Example

Step-by-Step

Let's find all the factor pairs for the number 20.

1. Start with 1. What do you multiply 1 by to get 20? 1 x 20 = 20. So, (1, 20) is a factor pair.
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2. Move to 2. What do you multiply 2 by to get 20? 2 x 10 = 20. So, (2, 10) is a factor pair.
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3. Try 3. Can you multiply 3 by a whole number to get 20? No. So, 3 is not a factor.
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4. Move to 4. What do you multiply 4 by to get 20? 4 x 5 = 20. So, (4, 5) is a factor pair.
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5. Move to 5. We already found (4, 5). Since 5 is the next number after 4, and we already have 5 in a pair, we have found all unique factor pairs.
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Answer: The factor pairs for 20 are (1, 20), (2, 10), and (4, 5).

Why It Matters

Understanding factor pairs helps you break down numbers, which is super useful in maths for fractions and algebra. It's also important in computer programming for optimising code, and even in fields like engineering to divide tasks or resources efficiently.

Common Mistakes

MISTAKE: Forgetting to include (1, the number itself) as a factor pair. | CORRECTION: Always start finding factor pairs by checking if 1 multiplied by the number gives the original number. (1, number) is always a factor pair.

MISTAKE: Stopping too early, before finding all factor pairs. For example, for 24, only finding (1, 24) and (2, 12). | CORRECTION: Keep checking numbers sequentially (1, 2, 3, 4...) until you reach a number that has already appeared as the second number in a pair (or the square root of the number).

MISTAKE: Including numbers that don't multiply to the original number. For example, saying (3, 5) is a factor pair for 12. | CORRECTION: Always double-check by multiplying the two numbers in your pair. If their product is not the original number, it's not a factor pair.

Practice Questions

Try It Yourself

QUESTION: Find all factor pairs for the number 18. | ANSWER: (1, 18), (2, 9), (3, 6)

QUESTION: Which of these is NOT a factor pair for 30: (1, 30), (2, 15), (3, 10), (4, 7)? | ANSWER: (4, 7) because 4 x 7 = 28, not 30.

QUESTION: A shopkeeper wants to arrange 36 packets of biscuits in equal rows. List all the possible ways he can arrange them using factor pairs. | ANSWER: (1 row of 36), (2 rows of 18), (3 rows of 12), (4 rows of 9), (6 rows of 6), (9 rows of 4), (12 rows of 3), (18 rows of 2), (36 rows of 1). (Note: For arrangements, (4,9) and (9,4) are distinct ways of arranging)

MCQ

Quick Quiz

Which of the following is a factor pair for 24?

(2, 10)

(3, 8)

(4, 7)

(5, 6)

The Correct Answer Is:

The correct answer is (3, 8) because 3 multiplied by 8 equals 24. Options A, C, and D do not multiply to 24.

Real World Connection

In the Real World

When a chef in a restaurant needs to divide a large batch of ingredients, say 50 grams of spices, into equal smaller portions for different dishes, they use factor pairs. For example, they might divide it into 5 portions of 10 grams each (5, 10) or 2 portions of 25 grams each (2, 25). This helps in consistent recipe preparation.

Key Vocabulary

Key Terms

FACTOR: A number that divides another number exactly, leaving no remainder. | PRODUCT: The result you get when you multiply two or more numbers. | MULTIPLICATION: The process of repeatedly adding a number to itself. | WHOLE NUMBERS: Numbers without fractions or decimals (0, 1, 2, 3...).

What's Next

What to Learn Next

Great job learning about factor pairs! Next, you can explore 'Prime and Composite Numbers'. Understanding factor pairs is key to identifying if a number is prime (has only one factor pair: 1 and itself) or composite (has more than one factor pair).