Math Tutor Explains: What are the Factors of 2641?

As your math tutor, I’m here to guide you through the different types of factors of 2641. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 2641: 1, 19, 139, 2641

• Sum of Factors of 2641: 2800

• Negative Factors of 2641: -1, -19, -139, -2641

• Prime Factors of 2641: 19, 139

• Prime Factorization of 2641: 19^1 × 139^1

There are two main ways a math tutor would explain how to find the factors of 2641: 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 2641 step by step!

Factor pairs of 2641 are any two numbers that, when multiplied together, equal 2641. The question to ask is “what two numbers multiplied together equal 2641?” Every factor can be paired with another factor, and multiplying the two will result in 2641.

To find the factor pairs of 2641, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2641. 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 2641 by the smallest prime factor, in this case, 19:

2641 ÷ 19 = 139

19 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 2641. So, to finish the factor pair for 2641, you’d multiply 19 and 139 before pairing with 1:

19 x 139 = 2641

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 2641:

(1, 2641), (19, 139)

So, to list all the factors of 2641: 1, 19, 139, 2641

The negative factors of 2641 would be: -1, -19, -139, -2641

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 2641, we break it down step by step until only prime factors remain. Then, we express 2641 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 2641 only has a few differences from the above method of finding the factors of 2641. 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 2641:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2641. 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 2641 by the smallest prime factor, in this case, 19

2641 ÷ 19 = 139

19 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 2641 are: 19, 139

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

Factors of 138 - The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138

Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

Factors of 22 - The factors of 22 are 1, 2, 11, 22

Factors of 93 - The factors of 93 are 1, 3, 31, 93