Question

Write 1859 as a product of prime factors.
Enter your answer as a product of prime numbers,
like 2 x 3, or as a single prime number, like 17.​

Answer 1

Step-by-step explanation:

Finding the prime factors of 1,859

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 1,859 by 2

1,859 ÷ 2 = 929.5 - This has a remainder. Let's try another prime number.

1,859 ÷ 3 = 619.6667 - This has a remainder. Let's try another prime number.

1,859 ÷ 5 = 371.8 - This has a remainder. Let's try another prime number.

1,859 ÷ 11 = 169 - No remainder! 11 is one of the factors!

169 ÷ 11 = 15.3636 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number

169 ÷ 13 = 13 - No remainder! 13 is one of the factors!

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

The orange divisor(s) above are the prime factors of the number 1,859. If we put all of it together we have the factors 11 x 13 x 13 = 1,859. It can also be written in exponential form as 111 x 132.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 1,859.

Answer 2

Step-by-step explanation:

11×169

13×143

Here is your answer.