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'HCF using product notation' for 8th grade
8th grade / Number / Multiples Factors Primes / Factors / HCF using product notation
Find the highest common factor (HCF) of pairs of numbers using prime factorization and product notation
The highest common factor (HCF) of two numbers is the largest factor that is common to both numbers. It is also known as the Greatest Common Factor (GCF).
Product notation is a way of representing a number as a product of its prime factors. For example, the prime factorization of 24 can be written as 2³ × 3¹. To find the HCF of two or more numbers using product notation, you need to follow these steps:
- Write the prime factorization of each number using product notation.
- Identify the common factors of the two numbers
- Take the lower power of each factor that appears in both of the factorizations.
- Multiply the common factors together to get the HCF.
Example 1: Find the HCF of 18 and 24.
The prime factorization of 18 is:18 = 2¹ x 3²
The prime factorization of 24 is:24 = 2³ x 3¹
To find the HCF of 18 and 24, we take the lowest power of each prime factor that appears in both factorizations:
HCF(18,24) = 2¹ × 3¹ = 6
Example 2: Find the HCF of 16 and 28.
The prime factorization of 16 is:16 = 2⁴
The prime factorization of 28 is:28 = 2² x 7¹
To find the HCF of 16 and 28, we take the lower power of each prime factor that appears in both factorizations:
HCF(16,28) = 2² = 4
In this topic you are asked to find the highest common factor of pairs of numbers presenting your answers in product notation.
With these interactive math lessons you will be learning "HCF using product notation" from
8th grade / Number / Multiples Factors Primes in 3 easy steps. The math in our lessons consists of 6 questions that ask you to identify the Highest Common Factor (HCF) using product notation for the given pairs of numbers.
There are 3 easy math lesson activities in this "HCF using product notation" tutorial. These activities progress step by step to help you the learner gradually master this math topic. The activities are based on "3 stage questioning", a method of learning that quickly and easily builds your confidence as you work through the short series of lessons that strengthen your knowledge of the math that you want to learn.
When you have completed the tutorial for a topic, you should try some of our games before finally doing the test for your chosen topic. See the Help box below for detailed instructions on how to use the lesson activities to help you learn your math more easily.
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'HCF using product notation' for 8th grade
Introduction to the math topic
You start the tutorial with a lesson that introduces the math you will be learning. You will see a set of questions one at a time, and for each question you will see the written answer and also hear the answer to that question.
Repeat the question/answer by clicking on the brown speaker sign. Repeat the question/answer and expand the question graphic by clicking on the question box. Move between questions using the arrow buttons below the question. If there is additional information available for your chosen topic, the "i" button on the left upright bar will be brown on white. Click on the button to load the additional lesson information into the main interface.
Either / Or math lesson
This lesson moves on from the "Introduction" lesson and offers you two possible answers to each question. So, you will see a question then a voice will ask "Is this ... or is it ..." and you will have to choose which of the answers is the one that matches the question.
You choose an answer by clicking or tapping on one of the two answer boxes below the question. You can play the audio for each answer again by clicking on the speaker icon beside the written answer (if robot speech is available and enabled). The program will let you know each time whether you answered correctly. A star will light up red for a wrong answer or white/black for a correct answer.
This lesson asks you the questions in a random order compared to the introduction. At the end of the lesson, you can choose whether to repeat the lesson or move on to the next one.
What is it? math lesson
The final lesson of the tutorial shows you multiple possible answers for each question - you must choose the correct one. You are asked a question and below it are a list of two, three, or four possible written/numeric answers from this topic. Pressing the speaker icon will play the math audio for that answer.
For each picture, click on the answer that matches the question. The program will tell you whether you are right or not. As with the Either / Or activity a system of stars indicate your right and wrong answers. The What is it? lesson will show you all the questions you learned in the Introduction but in a random order.
When you complete the "What is it?" lesson, you can choose whether to go on to play some games with this topic, or whether you want to repeat some or all of the lesson activities in this tutorial. You should expect to get 80% of the answers correct in most of the activities before trying some of the Math games with this topic.
