Factors and Multiples Lesson  - Definition, Differences, and Examples

Lesson Overview

• What Are Factors and Multiples?
• Key Differences Between Factors and Multiples
• How to Find Factors and Multiples
• Factors and Multiples Examples

Numbers are the building blocks of mathematics, and two fundamental concepts: factors and multiples help in understanding the relationships of these numbers to understand deeper mathematical concepts. 

Understanding factors and multiples is crucial for various mathematical skills. They are essential for working with fractions, finding prime numbers, and simplifying expressions. These concepts also lay the groundwork for algebra and more advanced mathematical topics.

What Are Factors and Multiples?

Factors are the numbers that fit perfectly inside another number.  These numbers divide evenly into another number. Imagine dividing a pizza into equal slices. Each slice represents a factor.

• Example: The factors of 12 are like slicing a pizza into 1, 2, 3, 4, 6, or 12 equal slices.
  

Multiples are like skip-counting. Start with a number and keep adding it to itself. Each number you land on is a multiple. They are the results of multiplying a number by an integer.

Example: The first few multiples of 5 are 5, 10, 15, 20, and so on.

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Factors and Multiples Trivia Quiz Questions and Answers

Key Differences Between Factors and Multiples

While both relate to numbers, factors and multiples have distinct characteristics. Here's the difference between them - 

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FACTORS AND MULTIPLES EXERCISE [LEVEL 1]

How to Find Factors and Multiples

Factors are the numbers that divide evenly into another number and there are a few rules to find them. 

• Start with 1 and the number itself: Every number has at least two factors: 1 and itself.
  
• Divide by increasing numbers: Try dividing the number by 2, 3, 4, and so on. If it divides with no remainder, you've found a factor!
  
• Look for pairs: Factors often come in pairs. If 2 is a factor of 10, then 10 divided by 2 (which is 5) is also a factor.
  
• Stop when the numbers repeat: You can stop dividing when the factors start repeating.
  

Example: Find the factors of 18.

• Start with 1 and 18: 1 and 18 are factors.
• Divide by 2: 18 ÷ 2 = 9, so 2 and 9 are factors.
• Divide by 3: 18 ÷ 3 = 6, so 3 and 6 are factors.
• The next number is 6, which we already have, so we stop.

Therefore, the factors of 18 are 1, 2, 3, 6, 9, and 18.

There are two main rules to find multiples of a number - 

• Start with the number itself: The first multiple of any number is the number itself.
  
• Multiply by increasing integers: Multiply the number by 2, 3, 4, and so on. Each result is a multiple.
  

Example: Find the first 5 multiples of 4.

• Start with 4: The first multiple is 4.
• Multiply by 2: 4 x 2 = 8
• Multiply by 3: 4 x 3 = 12
• Multiply by 4: 4 x 4 = 16
• Multiply by 5: 4 x 5 = 20
  

Therefore, the first 5 multiples of 4 are 4, 8, 12, 16, and 20.

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MCQ on factors and multiples for class 6

Factors and Multiples Examples

Example 1: Find the factors of 36.

• Start with 1 and 36: 1 and 36 are factors.
• Divide by 2: 36 ÷ 2 = 18, so 2 and 18 are factors.
• Divide by 3: 36 ÷ 3 = 12, so 3 and 12 are factors.
• Divide by 4: 36 ÷ 4 = 9, so 4 and 9 are factors.
• Divide by 6: 36 ÷ 6 = 6, so 6 is a factor.

Therefore, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Example 2: Find the factors of 50.

• Start with 1 and 50: 1 and 50 are factors.
• Divide by 2: 50 ÷ 2 = 25, so 2 and 25 are factors.
• Divide by 5: 50 ÷ 5 = 10, so 5 and 10 are factors.

Therefore, the factors of 50 are 1, 2, 5, 10, 25, and 50.

Example 3: Find the factors of 7.

• Start with 1 and 7: 1 and 7 are factors.
• Try dividing by 2, 3, 4, 5, and 6: None of these divide evenly into 7.

Therefore, the factors of 7 are 1 and 7 (7 is a prime number).

Example 4: Find the first 6 multiples of 9.

• Start with 9: The first multiple is 9.
• Multiply by 2: 9 x 2 = 18
• Multiply by 3: 9 x 3 = 27
• Multiply by 4: 9 x 4 = 36
• Multiply by 5: 9 x 5 = 45
• Multiply by 6: 9 x 6 = 54

Therefore, the first 6 multiples of 9 are 9, 18, 27, 36, 45, and 54.

Example 5: Find the first 4 multiples of 12.

• Start with 12: The first multiple is 12.
• Multiply by 2: 12 x 2 = 24
• Multiply by 3: 12 x 3 = 36
• Multiply by 4: 12 x 4 = 48

Therefore, the first 4 multiples of 12 are 12, 24, 36, and 48.

Example 6: Find the first 10 multiples of 2.

• Start with 2: The first multiple is 2.
• Keep multiplying by increasing integers: 2 x 2 = 4, 2 x 3 = 6, 2 x 4 = 8, and so on.

Therefore, the first 10 multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.

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Math Trivia Quiz: Factors, Multiples, Divisibility, Prime and Composite Numbers!