Math Tutor Explains: What are the Factors of 2147?

As your math tutor, I’m here to guide you through the different types of factors of 2147. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 2147: 1, 19, 113, 2147

• Sum of Factors of 2147: 2280

• Negative Factors of 2147: -1, -19, -113, -2147

• Prime Factors of 2147: 19, 113

• Prime Factorization of 2147: 19^1 × 113^1

There are two main ways a math tutor would explain how to find the factors of 2147: 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 2147 step by step!

Factor pairs of 2147 are any two numbers that, when multiplied together, equal 2147. The question to ask is “what two numbers multiplied together equal 2147?” Every factor can be paired with another factor, and multiplying the two will result in 2147.

To find the factor pairs of 2147, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2147. 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 2147 by the smallest prime factor, in this case, 19:

2147 ÷ 19 = 113

19 and 113 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 113 as the new focus. Find the smallest prime factor that isn’t 1, and divide 113 by that number. In this case, 113 is the new smallest prime factor:

113 ÷ 113 = 1

Remember that this new factor pair is only for the factors of 113, not 2147. So, to finish the factor pair for 2147, you’d multiply 19 and 113 before pairing with 1:

19 x 113 = 2147

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 2147:

(1, 2147), (19, 113)

So, to list all the factors of 2147: 1, 19, 113, 2147

The negative factors of 2147 would be: -1, -19, -113, -2147

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 2147, we break it down step by step until only prime factors remain. Then, we express 2147 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 2147 only has a few differences from the above method of finding the factors of 2147. 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 2147:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2147. 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 2147 by the smallest prime factor, in this case, 19

2147 ÷ 19 = 113

19 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 113 as the new focus. Find the smallest prime factor that isn’t 1, and divide 113 by that number. The smallest prime factor you pick for 113 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 2147 are: 19, 113

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

Factors of 115 - The factors of 115 are 1, 5, 23, 115

Factors of 142 - The factors of 142 are 1, 2, 71, 142

Factors of 79 - The factors of 79 are 1, 79

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