Math Tutor Explains: What are the Factors of 1313?

As your math tutor, I’m here to guide you through the different types of factors of 1313. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 1313: 1, 13, 101, 1313

• Sum of Factors of 1313: 1428

• Negative Factors of 1313: -1, -13, -101, -1313

• Prime Factors of 1313: 13, 101

• Prime Factorization of 1313: 13^1 × 101^1

There are two main ways a math tutor would explain how to find the factors of 1313: 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 1313 step by step!

Factor pairs of 1313 are any two numbers that, when multiplied together, equal 1313. The question to ask is “what two numbers multiplied together equal 1313?” Every factor can be paired with another factor, and multiplying the two will result in 1313.

To find the factor pairs of 1313, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1313. 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 1313 by the smallest prime factor, in this case, 13:

1313 ÷ 13 = 101

13 and 101 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 101 as the new focus. Find the smallest prime factor that isn’t 1, and divide 101 by that number. In this case, 101 is the new smallest prime factor:

101 ÷ 101 = 1

Remember that this new factor pair is only for the factors of 101, not 1313. So, to finish the factor pair for 1313, you’d multiply 13 and 101 before pairing with 1:

13 x 101 = 1313

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 1313:

(1, 1313), (13, 101)

So, to list all the factors of 1313: 1, 13, 101, 1313

The negative factors of 1313 would be: -1, -13, -101, -1313

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 1313, we break it down step by step until only prime factors remain. Then, we express 1313 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 1313 only has a few differences from the above method of finding the factors of 1313. 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 1313:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1313. 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 1313 by the smallest prime factor, in this case, 13

1313 ÷ 13 = 101

13 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 101 as the new focus. Find the smallest prime factor that isn’t 1, and divide 101 by that number. The smallest prime factor you pick for 101 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 1313 are: 13, 101

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

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

Factors of 81 - The factors of 81 are 1, 3, 9, 27, 81

Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100

Factors of 49 - The factors of 49 are 1, 7, 49