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In this lesson, we will grasp the idea of factors, how to get factors, identifying if a number is a multiple of another number, and identifying whether a given number is a prime or composite.
See the fact file below for more information on the factors and multiples or alternatively, you can download our 29-page Factors and Multiples worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- Factors are the numbers we multiply together to get another number or the product/multiple.
- A number can have several factors.
- Factors are whole numbers. They are never fractions.
GETTING THE FACTORS OF A NUMBER
- We can start looking for factors by starting with 1 and the number. Let us use 120 as an example.
- We know that the product if we multiply 1 and a number is the number. Therefore, if we multiply 1 and 120, the answer is 120. Thus, 1 and 120 are factors of 120.
- 1, 120
- We cannot have a factor larger than the number itself.
- Now, starting from 1, we move forward.
- So, is 120 divisible by 2? Yes. And if we divide 120 by 2, the answer we will get is 60. Therefore, 2 and 60 are factors of 120.
- 1, 2, 60, 120
- Next, is 120 divisible by 3? Yes. If we divide 120 by 3, the answer we will get is 40. Thus, 3 and 40 are factors of 120.
- 1, 2, 3, 40, 60, 120
- Next, is 120 divisible by 4? Yes. And if we divide 120 by 4, the answer we will get is 30.
- 1, 2, 3, 4, 30, 40, 60, 120
- Next, we also know that 120 is divisible by 5. 5 times 24 is equal to 120.
- And, we also know that 120 is divisible by 6. 6 times 20 is equal to 120.
- Therefore, 5, 6, 20, and 24 are factors of 120.
- 1, 2, 3, 4, 5, 6, 20, 24, 30, 40, 60, 120
- Now, if we check if 120 is divisible by 7, the answer is no. Thus,7 is not a factor of 120.
- Moving on, 120 is divisible by 8. 120 divided by 8 is 15. But, we also know that 120 is not divisible by 9.
- Next, 120 is divisible by 10. And if we divide 120 by 10, the answer we will get is 12.
- 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- As you can see, we still haven’t tried 11. But we know that 120 is not divisible by 11. Therefore, we can already end our list.
- Thus, the numbers above are the factors of 120.
- Multiples, on the other hand, are different from factors.
- Multiples are the numbers we can get after multiplying a number by an integer.
- To find the multiples of 6, we need to multiply 6 by integers.
- Thus, based on the computations, the multiples of 6 are 6, 12, 18, 24, and 30.
- But that does not mean that these are the only multiples of 6.
- 66 is also a multiple of 6.
- Therefore, numbers divisible by 6 are considered as multiples of 6.
- Note that we can also have negative results.
- What are integers?
- Integers are numbers with no fractional part or decimals. Integers include counting numbers, zero, and the negative of counting numbers.
PRIME OR COMPOSITE
- In this section, we will try to understand what are prime numbers, what are composite numbers, and how to identify them.
- Prime Numbers
- Prime numbers have only two factors, 1 and the number itself.
- Composite Numbers
- Composite numbers have more than two factors.
- To achieve a better understanding, let’s use examples.
- The number five (5). What are the factors of 5?
- We know that to get five, the only numbers we can multiply are 1 and 5.
- 1, 5
- Therefore, the factors of five are only two: 1 and 5.
- Thus, 5 is a prime number.
- Next example, the number six (6).
- Let us use the factorization technique we used previously.
- Let us first list 1 and 6 as the initial factors, as it is already a given.
- Now, moving forward, let’s check if 2 is a factor of 6.
- Is 6 divisible by 2? Yes. We can multiply 2 and 3 to get 6.
- 1, 2, 3, 6
- From here, we can already determine that 6 has more than two factors. Therefore, it is a composite number.
Factors and Multiples Worksheets
This is a fantastic bundle which includes everything you need to know about the factors and multiples across 29 in-depth pages. These are ready-to-use Factors and Multiples worksheets that are perfect for teaching students about the idea of factors, how to get factors, identifying if a number is a multiple of another number, and identifying whether a given number is a prime or composite.
Complete List Of Included Worksheets
- Lesson Plan
- Factors and Multiples
- Finding Factors
- The Blanks
- M or F?
- Prime Numbers
- Pick One
- What’s the Answer?
- Let’s Go!
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Link will appear as Factors and Multiples Facts & Worksheets: https://kidskonnect.com - KidsKonnect, June 11, 2020
Use With Any Curriculum
These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.