Math Tutor Explains: What are the Factors of 1919?

As your math tutor, I’m here to guide you through the different types of factors of 1919. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 1919: 1, 19, 101, 1919

• Sum of Factors of 1919: 2040

• Negative Factors of 1919: -1, -19, -101, -1919

• Prime Factors of 1919: 19, 101

• Prime Factorization of 1919: 19^1 × 101^1

There are two main ways a math tutor would explain how to find the factors of 1919: 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 1919 step by step!

Factor pairs of 1919 are any two numbers that, when multiplied together, equal 1919. The question to ask is “what two numbers multiplied together equal 1919?” Every factor can be paired with another factor, and multiplying the two will result in 1919.

To find the factor pairs of 1919, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1919. 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 19.

Step 2:

Divide 1919 by the smallest prime factor, in this case, 19:

1919 ÷ 19 = 101

19 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 1919. So, to finish the factor pair for 1919, you’d multiply 19 and 101 before pairing with 1:

19 x 101 = 1919

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 1919:

(1, 1919), (19, 101)

So, to list all the factors of 1919: 1, 19, 101, 1919

The negative factors of 1919 would be: -1, -19, -101, -1919

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 1919, we break it down step by step until only prime factors remain. Then, we express 1919 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 1919 only has a few differences from the above method of finding the factors of 1919. 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 1919:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1919. 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 19.

Step 2:

Divide 1919 by the smallest prime factor, in this case, 19

1919 ÷ 19 = 101

19 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 1919 are: 19, 101

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

Factors of 134 - The factors of 134 are 1, 2, 67, 134

Factors of 127 - The factors of 127 are 1, 127

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

Factors of 125 - The factors of 125 are 1, 5, 25, 125