Math Tutor Explains: What are the Factors of 1807?

As your math tutor, I’m here to guide you through the different types of factors of 1807. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 1807: 1, 13, 139, 1807

• Sum of Factors of 1807: 1960

• Negative Factors of 1807: -1, -13, -139, -1807

• Prime Factors of 1807: 13, 139

• Prime Factorization of 1807: 13^1 × 139^1

There are two main ways a math tutor would explain how to find the factors of 1807: using factor pairs and prime factorization. Let’s explore both!

As your math tutor, I’m here to help you break down factor pairs of 1807 step by step!

Factor pairs of 1807 are any two numbers that, when multiplied together, equal 1807. The question to ask is “what two numbers multiplied together equal 1807?” Every factor can be paired with another factor, and multiplying the two will result in 1807.

To find the factor pairs of 1807, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1807. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 13.

Step 2:

Divide 1807 by the smallest prime factor, in this case, 13:

1807 ÷ 13 = 139

13 and 139 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 139 as the new focus. Find the smallest prime factor that isn’t 1, and divide 139 by that number. In this case, 139 is the new smallest prime factor:

139 ÷ 139 = 1

Remember that this new factor pair is only for the factors of 139, not 1807. So, to finish the factor pair for 1807, you’d multiply 13 and 139 before pairing with 1:

13 x 139 = 1807

Step 4:

Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.

Here are all the factor pairs for 1807:

(1, 1807), (13, 139)

So, to list all the factors of 1807: 1, 13, 139, 1807

The negative factors of 1807 would be: -1, -13, -139, -1807

Now you’ve got it! A math tutor would always encourage you to practice with different numbers to reinforce your understanding of factor pairs. Try another one!

To find the prime factorization of 1807, we break it down step by step until only prime factors remain. Then, we express 1807 as a product of these prime factors multiplied together. Let’s go through the process and simplify it like a math tutor would!

The process of finding the prime factorization of 1807 only has a few differences from the above method of finding the factors of 1807. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.

Here are the steps for finding the prime factorization of 1807:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1807. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 13.

Step 2:

Divide 1807 by the smallest prime factor, in this case, 13

1807 ÷ 13 = 139

13 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 139 as the new focus. Find the smallest prime factor that isn’t 1, and divide 139 by that number. The smallest prime factor you pick for 139 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.

So, the unique prime factors of 1807 are: 13, 139

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 7 - The factors of 7 are 1, 7

Factors of 146 - The factors of 146 are 1, 2, 73, 146

Factors of 137 - The factors of 137 are 1, 137

Factors of 61 - The factors of 61 are 1, 61