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Video 1
Video 1
You must know what a factor is to understand this page, please check the factors, prime factors and HCF page if you do not know. IT IS NOT HARD. WHEN WE TALK ABOUT FACTORS ON THIS PAGE, WE ARE TALKING ABOUT THE POSITIVE FACTORS OF A NUMBER. The aim is to write a number a product of its prime factors, prime factors are positive numbers and thus we only use positive factors.
A whole number has factors which can be prime. So factors which are prime numbers are called prime factors. In our example, of using 28, 7 and 4 are two factors of 28. 7 is one the prime factors because IT IS A FACTOR OF 28 AND A PRIME NUMBER.
So when we say product of prime factors, we are trying to attain all the factors which are prime for a whole number and find a way to multiply them to get 28.
28 has the following factors, 1, 2, 4, 7, 14, 28
The factors that are prime are 2 and 7, so we need to find a way to multiply the prime factors to get 28. We know that 2 x 2 x 7 = 28, so to express 28 as a product of its prime factors we would write 22 x 7 = 28
Now we know what it means to express a whole number as a product of its prime factors. Finding the factors of 28 was not that hard, it is simple multiplication, however for other numbers it can take longer and harder to think of factors, this is where we use the TECHNIQUE used in the video to find the product of the prime factors.
First find two positive factors of 28, except for 28 and 1. We chose 7 and 4. Now we have to evaluate these factors by determining which of these factors are prime.
Circle the prime factor if any, in our case we had 7 (this is our first prime factor that would form a part of the product that we are trying to find).
For the other non-prime factor which was 4, find two factors for 4 (except for 4 and 1), in our case we came up with 2 and 2.Now we have to evaluate these factors by determining which of these factors are prime.
2 is a prime number, so we can circle both 2s (both of these 2s would form a part of the product that we are trying to find).
We can see that as 2 prime number, we do not need to find two factors of 2 and thus we end with 3 circled numbers. So the process ends with prime numbers that multiply to get 28.
So now we have our product, 2 x 2 x 7 = 22 x 7 = 28. This shows how we have expressed 28 as a product of its prime factors.
There is no right or wrong way to start this method. For example, say if we had used 14 and 2 for the factors of 28. Then 2 would be circled, the non-prime factor which is 14 would be expressed using the factors of 14, 7 and 2, both are prime and so both would be circled. You can see that the prime factors of 28 would still be 2 and 7, and the numbers that we would circle are 7 and two 2s.
2 x 2 x 7 = 28 = 22 x 7 (We have written 28 as a product of its prime factors)
Knowing how to identify the product of a whole number's prime factors are extremely important, when working out the HCF and LCM of two or more common numbers. This is explained in the next page, if you understood this page you have already started to work on understanding HCF and LCM, as we use the same technique.
Video 1 Explanation
Video 1 Explanation
A whole number has factors which can be prime. So factors which are prime numbers are called prime factors. In our example, of using 28, 7 and 4 are two factors of 28. 7 is one the prime factors because IT IS A FACTOR OF 28 AND A PRIME NUMBER.
So when we say product of prime factors, we are trying to attain all the factors which are prime for a whole number and find a way to multiply them to get 28.
28 has the following factors, 1, 2, 4, 7, 14, 28
The factors that are prime are 2 and 7, so we need to find a way to multiply the prime factors to get 28. We know that 2 x 2 x 7 = 28, so to express 28 as a product of its prime factors we would write 22 x 7 = 28
Now we know what it means to express a whole number as a product of its prime factors. Finding the factors of 28 was not that hard, it is simple multiplication, however for other numbers it can take longer and harder to think of factors, this is where we use the TECHNIQUE used in the video to find the product of the prime factors.
First find two positive factors of 28, except for 28 and 1. We chose 7 and 4. Now we have to evaluate these factors by determining which of these factors are prime.
Circle the prime factor if any, in our case we had 7 (this is our first prime factor that would form a part of the product that we are trying to find).
For the other non-prime factor which was 4, find two factors for 4 (except for 4 and 1), in our case we came up with 2 and 2.Now we have to evaluate these factors by determining which of these factors are prime.
2 is a prime number, so we can circle both 2s (both of these 2s would form a part of the product that we are trying to find).
We can see that as 2 prime number, we do not need to find two factors of 2 and thus we end with 3 circled numbers. So the process ends with prime numbers that multiply to get 28.
So now we have our product, 2 x 2 x 7 = 22 x 7 = 28. This shows how we have expressed 28 as a product of its prime factors.
There is no right or wrong way to start this method. For example, say if we had used 14 and 2 for the factors of 28. Then 2 would be circled, the non-prime factor which is 14 would be expressed using the factors of 14, 7 and 2, both are prime and so both would be circled. You can see that the prime factors of 28 would still be 2 and 7, and the numbers that we would circle are 7 and two 2s.
2 x 2 x 7 = 28 = 22 x 7 (We have written 28 as a product of its prime factors)
Knowing how to identify the product of a whole number's prime factors are extremely important, when working out the HCF and LCM of two or more common numbers. This is explained in the next page, if you understood this page you have already started to work on understanding HCF and LCM, as we use the same technique.
Figure 1
Lets try and write the number 36 has a product of its prime factors. This shown in figure 1.
Two factors of 36, which we start with are 12 and 3.
We need to evaluate which of these factors are prime. Is 12 a prime number? NO. Is 3 a prime number? Yes
3 is a prime number, and thus it is circled (the prime factor 3 would therefore form a part of our product that we are trying to find).
12 is not a prime number, so we need to find two factors of 12 (except for 12 and 1). We can choose 4 and 3.
Now we have to determine which of the factors of 12 are prime.
3 is a prime number and thus it is circled (the prime factor 3 would therefore form a part of our product that we are trying to find).
However 4 is not, so we need to find two factors of 4 (except for 4 and 1). We can choose 2 and 2. The number 2 is a prime number and as there are two 2s we can circle both (both twos would form a part of our product we are trying to find).
So 36 = 3 x 3 x 3 x 2 = 32 x 22 (we have written 36 as a product of its prime factors)The process stops when we do not need to find anymore factors, because every number is broken up until we end with just prime factors. Take a look at the next example to understand this better.
Two factors of 36, which we start with are 12 and 3.
We need to evaluate which of these factors are prime. Is 12 a prime number? NO. Is 3 a prime number? Yes
3 is a prime number, and thus it is circled (the prime factor 3 would therefore form a part of our product that we are trying to find).
12 is not a prime number, so we need to find two factors of 12 (except for 12 and 1). We can choose 4 and 3.
Now we have to determine which of the factors of 12 are prime.
3 is a prime number and thus it is circled (the prime factor 3 would therefore form a part of our product that we are trying to find).
However 4 is not, so we need to find two factors of 4 (except for 4 and 1). We can choose 2 and 2. The number 2 is a prime number and as there are two 2s we can circle both (both twos would form a part of our product we are trying to find).
So 36 = 3 x 3 x 3 x 2 = 32 x 22 (we have written 36 as a product of its prime factors)The process stops when we do not need to find anymore factors, because every number is broken up until we end with just prime factors. Take a look at the next example to understand this better.
Figure 2
We need to write the number 72 as a product of its prime factors.
Two factors of 72 (except for 72 and 1) which we can choose are 12 and 6.
Now we have to determine whether these factors are prime or not. Both 12 and 6 are not prime numbers. So we need to find two factors for both 12 and 6.
Two factors of 12 (except 12 and 1) we can choose are 4 and 3. Now we have to evaluate whether the factors are prime or not.
3 is a prime number and thus would be circled (therefore, the number 3 would form a part of our product that we are trying to find).
4 is not a prime number, thus we need to find two factors of 4 (except 4 and 1). We can choose 2 and 2. Now we have to evaluate whether the factors are prime or not. As 2 is a prime number, we can circle both 2s (both 2s would therefore form a part of our product that we are trying to find).
Two factors of 6 (except 6 and 1) we can choose are 3 and 2. Now we have to evaluate whether the factors are prime or not.
Both 3 and 2 are prime, so both numbers would be circled (therefore both 3 and 2 would form a part of our product that we are trying to find).
All of our circled numbers are 2, 2, 3, 3, 2 and 2. So
2 x 2 x 2 x 2 x 3 x 3 = 24 x 32 = 72 (We have written 72 as a product of its prime factors)
We can see that in general and thus for all three examples on this page. the process ends with prime numbers (the circled numbers).
At each step, each factor will be evaluated by determining whether the factor is a prime number or not. if it is prime, we circle it, as this will be used in the product that we are trying to find, if not, we find two factors of the factor and determine whether these two factors are prime or not. This process is repeated, as shown in the three examples until we have just prime factors. When we have prime factors we circle them, and thus there is no need to find two factors of the prime factor. The process therefore then ends, when we just have prime factors. These will therefore form the product that we are trying to find.
Two factors of 72 (except for 72 and 1) which we can choose are 12 and 6.
Now we have to determine whether these factors are prime or not. Both 12 and 6 are not prime numbers. So we need to find two factors for both 12 and 6.
- Lets focus on the number 12 first. Which number you focus on first is your choice.
Two factors of 12 (except 12 and 1) we can choose are 4 and 3. Now we have to evaluate whether the factors are prime or not.
3 is a prime number and thus would be circled (therefore, the number 3 would form a part of our product that we are trying to find).
4 is not a prime number, thus we need to find two factors of 4 (except 4 and 1). We can choose 2 and 2. Now we have to evaluate whether the factors are prime or not. As 2 is a prime number, we can circle both 2s (both 2s would therefore form a part of our product that we are trying to find).
- Now lets focus on the number 6.
Two factors of 6 (except 6 and 1) we can choose are 3 and 2. Now we have to evaluate whether the factors are prime or not.
Both 3 and 2 are prime, so both numbers would be circled (therefore both 3 and 2 would form a part of our product that we are trying to find).
All of our circled numbers are 2, 2, 3, 3, 2 and 2. So
2 x 2 x 2 x 2 x 3 x 3 = 24 x 32 = 72 (We have written 72 as a product of its prime factors)
We can see that in general and thus for all three examples on this page. the process ends with prime numbers (the circled numbers).
At each step, each factor will be evaluated by determining whether the factor is a prime number or not. if it is prime, we circle it, as this will be used in the product that we are trying to find, if not, we find two factors of the factor and determine whether these two factors are prime or not. This process is repeated, as shown in the three examples until we have just prime factors. When we have prime factors we circle them, and thus there is no need to find two factors of the prime factor. The process therefore then ends, when we just have prime factors. These will therefore form the product that we are trying to find.
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