You are watching: What is the prime factorization of 33

## Why is the prime factorization the 33 created as 31 x 111?

### What is element factorization?

**Prime factorization** or **prime factor decomposition** is the process of recognize which prime numbers can be multiplied together to make the initial number.

### Finding the prime factors of 33

To find the element factors, you begin by separating the number by the an initial prime number, i m sorry is 2. If there **is not** a remainder, meaning you can divide evenly, climate 2 is a element of the number. Continue dividing by 2 till you cannot division evenly anymore. Create down how many 2"s you were able to division by evenly. Now try dividing through the following prime factor, i beg your pardon is 3. The score is to acquire to a quotient of 1.

If that doesn"t make feeling yet, let"s try it...

Here room the very first several element factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let"s begin by dividing 33 by 2

33 ÷ 2 = 16.5 - This has a remainder. Let"s try another element number.33 ÷ 3 = 11 - No remainder! 3 is just one of the factors!11 ÷ 3 = 3.6667 - over there is a remainder. We can"t division by 3 evenly anymore. Let"s shot the next prime number11 ÷ 5 = 2.2 - This has actually a remainder. 5 is not a factor.11 ÷ 7 = 1.5714 - This has a remainder. 7 is no a factor.11 ÷ 11 = 1 - No remainder! 11 is among the factors!

The orange divisor(s) over are the prime determinants of the number 33. If we put every one of it with each other we have actually the components 3 x 11 = 33. That can also be created in exponential form as 31 x 111.

### Factor Tree

Another method to do prime factorization is to usage a element tree. Below is a aspect tree because that the number 33.

33 | ||

3 | 11 |

### More prime Factorization Examples

31 | 32 | 34 | 35 |

311 | 25 | 21 x 171 | 51 x 71 |

try the variable calculator

### Explore an ext about the number 33:

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