# What is the prime factorization of 144?

## How to use the tool

To calculate the prime factors of 144 enter a number in the field below and press decompose:

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## Answer to the Factorization of 144

The factorization of 144 is equal to 2 × 2 × 2 × 2 × 3 × 3. We find these factors by successively dividing 144 by the prime numbers until we obtain the prime factors.

## Factor Tree of 144

The prime factor tree of 144 is an illustration that shows how the number 144 is decomposed into its fundamental prime factors, as 2, 3 and 5. This visual representation helps you understand the underlying structure of the number and how it is formed from smaller prime numbers.

Look at the following tree:

 144 2 72 2 36 3 12 2 6 2 3

## Steps to Factor the Number 144

### 1. Division by Smaller Prime Numbers:

Start by dividing the number 144 by the smallest prime numbers, starting with the smallest prime, which is 2.

144 ÷ 2 = 72

### 2. Continuação das Divisões:

Agora, continue dividindo o resultado da etapa anterior por números primos menores, até que não seja mais possível fazer divisões inteiras.

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 3 = 3

### 3. Continuação das Divisões:

Continue as divisões até não ser mais possível obter divisões inteiras.

3 ÷ 3 = 1

### 4. Obtenção dos Fatores Primos:

Now, the numbers by which you divided 144 and got integer results are the prime factors of 144. In this case, we have 2, 2, 2, 2, 3 and 3.

### 5. Expressão da Fatoração:

Write the factorization of the number 144 using its prime factors. The full factorization of 144 is:

144 = 2 × 2 × 2 × 2 × 3 × 3

These steps show how the number 144 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.