How to Make a Factor Tree Step by Step with Examples
The diagram used to calculate the prime factors of a natural number greater than one is a Factor Tree.
Factor Tree Method
Basic steps in the Factor Tree Method as follows:
In constructing a Factor Tree, the first step is to find a pair of factors whose product is the number we are factoring in. The first branch in the Factor Tree is these two variables.
There are often several distinct pairs of variables that we might choose to start the process. Here we can start with any two variables.
For each factor, we repeat the process until every tree branch ends in a primary. The prime factorization is done then.
The Fundamental Theorem of Arithmetic ensures that the same, unique prime factorization for the number can result in all prime factorizations of the same number.
For example, the number 30 can be written as 2 x 3 x 5 in prime factorization which is found by Factor Tree method as follows:
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Prime Factorization By Factor Tree Method
Prime factorization is a method of factoring a number in terms of prime numbers, i.e. finding a number's prime factors, so that these factors will equally divide the original number.
The Prime Factorization will use Division method or Factor Tree method to find the Prime factors of any numbers.
The logic behind Prime factorization is to divide the given number by prime factors until we get the remainder as equal to 1.
36 Factor Tree
The Prime Factor Tree for 36 is given as below:
Step 1: Divide 36 by the lowest prime number. Here we are dividing by 2.
Step 2: After dividing 36 by 2 we get 18, divide again by the lowest prime number. Here we will divide by 2 again.
Step 3: After dividing 18 by 2 we get 9, the lowest prime number which divides 9 is 3. So we get 3 and dividing it again by 3 we will get the remainder as 1. So this will give us the Prime Factorization by Factor Tree method.
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The prime factorization of 36 from the Prime FactorizationTree Method is 2 x 2 x 3 x 3.
Factor Tree of 65
The Prime Factor Tree for 65 is given as below:
Step 1: Divide 65 by the lowest prime factor. Here 65 is divisible by 5 which will give 13.
Step 2: So 13 is only divisible by 13 which will give the remainder as 1. So this will give us the Prime Factorization by Factor Tree method.
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The prime factorization of 65 from the Prime Factorization Tree Method is 5 x 13.
Factor Tree Method of 48
The Prime Factor Tree for 48 is given as below:
Step 1: Divide the number 48 by the least possible prime factor. Here 48 is divisible by 2 which gives 24.
Step 2: Divide 24 again by 2 which will give us 12.
Step 3: Divide 12 by 2 which will give us 6.
Step 4: Dividing 6 by 2 we will get the remainder as 3.
Step 5: Since we have to get the final remainder as 1 divide 3 by 3. So this will give us the Prime Factorization by Factor Tree method.
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The prime factorization of 48 from the Prime Factorization Tree Method is 2 x 2 x 2 x 2 x 3.
Conclusion
We can conclude by saying that the Factor Tree is a diagrammatic method used to determine the prime factors of any natural number greater than one. This is one of the simplest and easiest methods to find Prime factorization of any numbers.
FAQs on Factor Tree for Finding Prime Factors
1. What is a factor tree in maths?
A factor tree is a diagram used to break a number down into its prime factors. It starts with a composite number and splits it into two smaller factors, and each factor is then broken down further until only prime numbers remain. A factor tree helps in finding the prime factorization of a number in a clear, step-by-step way.
2. How do you make a factor tree step by step?
To make a factor tree, divide the number into factors and continue until all factors are prime numbers.
- Start with a composite number (e.g., 24).
- Split it into two factors (e.g., 4 × 6).
- Break down each factor further (4 = 2 × 2, 6 = 2 × 3).
- Stop when all branches end in prime numbers.
3. What is the purpose of a factor tree?
The purpose of a factor tree is to find the prime factorization of a number. It helps students understand how numbers are built from prime numbers and is commonly used to calculate the HCF (Highest Common Factor) and LCM (Least Common Multiple).
4. Can you give an example of a factor tree?
Yes, a factor tree for 18 shows its prime factorization as 2 × 3 × 3.
- Start with 18.
- Split into 2 × 9.
- Break 9 into 3 × 3.
- All end numbers (2, 3, 3) are prime.
5. What are prime factors in a factor tree?
Prime factors are the prime numbers at the ends of a factor tree. A prime number has exactly two factors: 1 and itself. In a factor tree, you continue splitting numbers until only prime numbers remain, and their product gives the original number.
6. Is there only one correct factor tree for a number?
No, there can be different factor trees for the same number, but they all give the same prime factorization. For example, 16 can be split as 2 × 8 or 4 × 4 first, but both methods end with 2 × 2 × 2 × 2 or 2⁴.
7. How do you use a factor tree to find the HCF?
You use factor trees to find the HCF by identifying common prime factors of two or more numbers.
- Find the prime factorization of each number using factor trees.
- Circle the common prime factors.
- Multiply the common primes together.
8. How do you use a factor tree to find the LCM?
You use factor trees to find the LCM by taking all prime factors with the highest powers.
- Find the prime factorization of each number.
- Select each prime factor with its greatest exponent.
- Multiply them together.
9. What is the difference between a factor tree and a factor list?
A factor tree shows the prime factorization of a number, while a factor list shows all its factors. For example, the factor tree of 12 gives 2 × 2 × 3, while the factor list of 12 is 1, 2, 3, 4, 6, and 12.
10. What are common mistakes when drawing a factor tree?
Common mistakes in a factor tree include stopping before reaching prime numbers or using incorrect factors.
- Not breaking numbers down to prime numbers.
- Using incorrect multiplication pairs.
- Forgetting to include repeated prime factors.
