A: The prime components are: 3 x 19 or likewise written as 3, 19 composed in exponential form: 31 x 191

## Why is the prime factorization of 57 created as 31 x 191?

### What is element factorization?

Prime factorization or prime aspect decomposition is the process of recognize which prime numbers have the right to be multiplied with each other to make the initial number.

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### Finding the prime determinants of 57

To uncover the element factors, you start by splitting the number by the an initial prime number, i beg your pardon is 2. If over there is not a remainder, definition you have the right to divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot division evenly anymore. Write down how many 2"s you to be able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

If the doesn"t make sense yet, let"s shot it...

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

Let"s start by splitting 57 by 2

57 ÷ 2 = 28.5 - This has a remainder. Let"s shot another prime number.57 ÷ 3 = 19 - No remainder! 3 is just one of the factors!19 ÷ 3 = 6.3333 - there is a remainder. We can"t divide by 3 same anymore. Let"s shot the following prime number19 ÷ 5 = 3.8 - This has actually a remainder. 5 is no a factor.19 ÷ 7 = 2.7143 - This has a remainder. 7 is not a factor.19 ÷ 11 = 1.7273 - This has a remainder. 11 is no a factor....Keep trying significantly larger numbers until you uncover one the divides evenly.

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...19 ÷ 19 = 1 - No remainder! 19 is just one of the factors!

The orange divisor(s) above are the prime determinants of the number 57. If we put all of it with each other we have actually the factors 3 x 19 = 57. It can also be created in exponential type as 31 x 191.

### Factor Tree

Another means to execute prime factorization is to usage a aspect tree. Below is a element tree because that the number 57.

 57 3 19

### More prime Factorization Examples

 55 56 58 59 51 x 111 23 x 71 21 x 291 591

try the factor calculator