Factor Tree

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.