Math Tutor Explains: What are the Factors of 1937?

As your math tutor, I’m here to guide you through the different types of factors of 1937. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 1937: 1, 13, 149, 1937

• Sum of Factors of 1937: 2100

• Negative Factors of 1937: -1, -13, -149, -1937

• Prime Factors of 1937: 13, 149

• Prime Factorization of 1937: 13^1 × 149^1

There are two main ways a math tutor would explain how to find the factors of 1937: 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 1937 step by step!

Factor pairs of 1937 are any two numbers that, when multiplied together, equal 1937. The question to ask is “what two numbers multiplied together equal 1937?” Every factor can be paired with another factor, and multiplying the two will result in 1937.

To find the factor pairs of 1937, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1937. 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 1937 by the smallest prime factor, in this case, 13:

1937 ÷ 13 = 149

13 and 149 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 149 as the new focus. Find the smallest prime factor that isn’t 1, and divide 149 by that number. In this case, 149 is the new smallest prime factor:

149 ÷ 149 = 1

Remember that this new factor pair is only for the factors of 149, not 1937. So, to finish the factor pair for 1937, you’d multiply 13 and 149 before pairing with 1:

13 x 149 = 1937

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 1937:

(1, 1937), (13, 149)

So, to list all the factors of 1937: 1, 13, 149, 1937

The negative factors of 1937 would be: -1, -13, -149, -1937

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 1937, we break it down step by step until only prime factors remain. Then, we express 1937 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 1937 only has a few differences from the above method of finding the factors of 1937. 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 1937:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1937. 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 1937 by the smallest prime factor, in this case, 13

1937 ÷ 13 = 149

13 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 149 as the new focus. Find the smallest prime factor that isn’t 1, and divide 149 by that number. The smallest prime factor you pick for 149 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 1937 are: 13, 149

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

Factors of 105 - The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

Factors of 139 - The factors of 139 are 1, 139

Factors of 29 - The factors of 29 are 1, 29

Factors of 97 - The factors of 97 are 1, 97