Question

find the prime factors for the following numbers 156​

Answer 1

Answer:

2 x 2 x 3 x 13. 

hope this will help you

Answer 2

Step-by-step explanation:

Why is the prime factorization of 156 written as 22 x 31 x 131?

What is prime factorization?

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

Finding the prime factors of 156

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were 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 it doesn't make sense yet, let's try it...

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

Let's start by dividing 156 by 2

156 ÷ 2 = 78 - No remainder! 2 is one of the factors!

78 ÷ 2 = 39 - No remainder! 2 is one of the factors!

39 ÷ 2 = 19.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number

39 ÷ 3 = 13 - No remainder! 3 is one of the factors!

13 ÷ 3 = 4.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number

13 ÷ 5 = 2.6 - This has a remainder. 5 is not a factor.

13 ÷ 7 = 1.8571 - This has a remainder. 7 is not a factor.

13 ÷ 11 = 1.1818 - This has a remainder. 11 is not a factor.

13 ÷ 13 = 1 - No remainder! 13 is one of the factors!

The orange divisor(s) above are the prime factors of the number 156. If we put all of it together we have the factors 2 x 2 x 3 x 13 = 156. It can also be written in exponential form as 22 x 31 x 131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 156.

156

Factor Arrows

2 78

Factor Arrows

2 39

Factor Arrows

3 13

More Prime Factorization Examples

154 155 157 158

21 x 71 x 111 51 x 311 1571 21 x 791