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Secondary math tests for
'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 our quick math tests you will be revising "HCF using product notation" in 2 simple steps. The math in our tests consists of 16 questions that ask you to identify the Highest Common Factor (HCF) using product notation for the given pairs of numbers.
These math tests are designed to round off your learning experience here at Free Math Games by testing whether you can correctly recognize the math you have learned (in the multiple choice test) and that you can correctly enter the correct answers (in the writing test).
Make sure you have chosen the correct topic before starting! Although these tests are timed, try to relax and concentrate on getting the answers right at first - later you can try the tests again more quickly.
The two types of tests are:
- A multiple choice quiz to check your recall of the math
- A writing test to check your math for the selected topic
Key features of our math tests include:
- You can do these tests at home (or at school) without the help of a teacher
- You can repeat our tests as often as you need to improve your scores
- The tests check your comprehension for the topic
- The writing test also checks your ability to write / type math answers for the topic
- The tests use all the questions in a topic, so you will see questions that weren't in the lessons
You should expect to score 8+ / 10 in each test before you select a new topic. It is a good idea to repeat the test for each topic you do after two weeks to "reinforce" the math for that topic
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How to use our math tests for
'HCF using product notation' for 8th grade
- On the settings screen, select the test you would like to take.
- A new screen will open with information concerning the test.
- When you are ready to begin, click "Start the test".
Multiple choice test
This is a multiple choice activity similar to "What is it" in the Math lessons - you are shown a randomly selected question from the topic you are using. A selection of topic answers are displayed as a list. If you click/tap the speaker beside any answer you will hear the audio for that answer.
For each question, you must click on the answer that matches that question. If your answer is correct you will hear a bell and one star will be lit. The next question will be shown. If your answer is wrong, a box will open showing you what the correct answer was.
The test is timed, and the clock starts when you click the Start button. The clock stops when you click your final answer. At the end of your test a screen will tell you how many of the questions you got right and how long you took to complete the test.
Writing test
The writing test checks whether you can type the correct answer using your keyboard. This test is also timed. You can do the test many times until you get a good score. To start the test, click on the "Writing test" sign in the navigation board, then click on the "Start the test" arrow.
A random problem from your selected topic is shown. Beneath the problem there is a white box into which you should type the answer. If you need a little help you can click on the "Help me" button for a tip. Only use the help if you really need to.
If you type the answer correctly your device will automatically light a star. If you have entered your answer and no star lights up, click on the tick or press Enter to check your answer. When you have tried all the questions, a screen will show you how many questions you answered correctly and how long it took.
* Try to score 8 out of 10 in both test before you choose a new topic *
* It is OK to do the tests many times if you need to *
