Math Tutor Explains: What are the Factors of 316?

As your math tutor, I’m here to guide you through the different types of factors of 316. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 316: 1, 2, 4, 79, 158, 316

• Sum of Factors of 316: 560

• Negative Factors of 316: -1, -2, -4, -79, -158, -316

• Prime Factors of 316: 2, 79

• Prime Factorization of 316: 2^2 × 79^1

There are two main ways a math tutor would explain how to find the factors of 316: 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 316 step by step!

Factor pairs of 316 are any two numbers that, when multiplied together, equal 316. The question to ask is “what two numbers multiplied together equal 316?” Every factor can be paired with another factor, and multiplying the two will result in 316.

To find the factor pairs of 316, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 316. 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 316 by the smallest prime factor, in this case, 2:

316 ÷ 2 = 158

2 and 158 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 158 as the new focus. Find the smallest prime factor that isn’t 1, and divide 158 by that number. In this case, 2 is the new smallest prime factor:

158 ÷ 2 = 79

Remember that this new factor pair is only for the factors of 158, not 316. So, to finish the factor pair for 316, you’d multiply 2 and 2 before pairing with 79:

2 x 2 = 4

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 316:

(1, 316), (2, 158), (4, 79)

So, to list all the factors of 316: 1, 2, 4, 79, 158, 316

The negative factors of 316 would be: -1, -2, -4, -79, -158, -316

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 316, we break it down step by step until only prime factors remain. Then, we express 316 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 316 only has a few differences from the above method of finding the factors of 316. 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 316:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 316. 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 316 by the smallest prime factor, in this case, 2

316 ÷ 2 = 158

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 158 as the new focus. Find the smallest prime factor that isn’t 1, and divide 158 by that number. The smallest prime factor you pick for 158 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 316 are: 2, 79

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

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

Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28

Factors of 110 - The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110

Factors of 38 - The factors of 38 are 1, 2, 19, 38