How to Create a Factor Tree: A Step-by-Step Guide for Finding Prime Factors

Factor tree

A factor tree is a visual representation of the prime factors of a number

A factor tree is a visual representation of the prime factors of a number. It helps in finding all the prime factors of a given number and breaking it down into its prime factorization.

Let’s take an example to understand how to create a factor tree:

Example: Factor tree for the number 72

1. Start by writing the number you want to factorize at the top of the tree, in this case, 72.

72

2. Begin by finding a pair of factors of the given number that are prime. The factors of 72 are 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. We can observe that 2 and 3 are prime factors.

72
/\
2 36

3. Choose one of the factors and split it into its prime factors. In this case, let’s split 36.

72
/\
2 36
/\
2 18

4. Repeat the process for the remaining numbers until all the resulting factors are prime numbers. In this case, we split 18.

72
/\
2 36
/\
2 18
/\
2 9

5. Continue splitting until we have only prime factors left. Split 9 into 3 and 3.

72
/\
2 36
/\
2 18
/\
2 9
/\
3 3

6. Once we only have prime factors left, we can stop splitting. The factors of 72 are now represented at the bottom of the tree.

72
/\
2 36
/\
2 18
/\
2 9
/\
3 3

7. The prime factors of 72 are 2, 2, 2, 3, and 3. We can write the prime factorization of 72 as 2^3 * 3^2.

Therefore, the factor tree for the number 72 is represented by the branches of the tree:
2
/ \
2 2
/ \
2 3
\
3

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