Math Tutor Explains: What are the Factors of 474?

As your math tutor, I’m here to guide you through the different types of factors of 474. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 474: 1, 2, 3, 6, 79, 158, 237, 474

• Sum of Factors of 474: 960

• Negative Factors of 474: -1, -2, -3, -6, -79, -158, -237, -474

• Prime Factors of 474: 2, 3, 79

• Prime Factorization of 474: 2^1 × 3^1 × 79^1

There are two main ways a math tutor would explain how to find the factors of 474: 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 474 step by step!

Factor pairs of 474 are any two numbers that, when multiplied together, equal 474. The question to ask is “what two numbers multiplied together equal 474?” Every factor can be paired with another factor, and multiplying the two will result in 474.

To find the factor pairs of 474, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 474. 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 2.

Step 2:

Divide 474 by the smallest prime factor, in this case, 2:

474 ÷ 2 = 237

2 and 237 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 237 as the new focus. Find the smallest prime factor that isn’t 1, and divide 237 by that number. In this case, 3 is the new smallest prime factor:

237 ÷ 3 = 79

Remember that this new factor pair is only for the factors of 237, not 474. So, to finish the factor pair for 474, you’d multiply 2 and 3 before pairing with 79:

2 x 3 = 6

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 474:

(1, 474), (2, 237), (3, 158), (6, 79)

So, to list all the factors of 474: 1, 2, 3, 6, 79, 158, 237, 474

The negative factors of 474 would be: -1, -2, -3, -6, -79, -158, -237, -474

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 474, we break it down step by step until only prime factors remain. Then, we express 474 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 474 only has a few differences from the above method of finding the factors of 474. 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 474:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 474. 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 2.

Step 2:

Divide 474 by the smallest prime factor, in this case, 2

474 ÷ 2 = 237

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 237 as the new focus. Find the smallest prime factor that isn’t 1, and divide 237 by that number. The smallest prime factor you pick for 237 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 474 are: 2, 3, 79

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

Factors of 33 - The factors of 33 are 1, 3, 11, 33

Factors of 101 - The factors of 101 are 1, 101

Factors of 85 - The factors of 85 are 1, 5, 17, 85

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