Math Tutor Explains: What are the Factors of 370?

As your math tutor, I’m here to guide you through the different types of factors of 370. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 370: 1, 2, 5, 10, 37, 74, 185, 370

• Sum of Factors of 370: 684

• Negative Factors of 370: -1, -2, -5, -10, -37, -74, -185, -370

• Prime Factors of 370: 2, 5, 37

• Prime Factorization of 370: 2^1 × 5^1 × 37^1

There are two main ways a math tutor would explain how to find the factors of 370: 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 370 step by step!

Factor pairs of 370 are any two numbers that, when multiplied together, equal 370. The question to ask is “what two numbers multiplied together equal 370?” Every factor can be paired with another factor, and multiplying the two will result in 370.

To find the factor pairs of 370, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 370. 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 370 by the smallest prime factor, in this case, 2:

370 ÷ 2 = 185

2 and 185 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 185 as the new focus. Find the smallest prime factor that isn’t 1, and divide 185 by that number. In this case, 5 is the new smallest prime factor:

185 ÷ 5 = 37

Remember that this new factor pair is only for the factors of 185, not 370. So, to finish the factor pair for 370, you’d multiply 2 and 5 before pairing with 37:

2 x 5 = 10

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 370:

(1, 370), (2, 185), (5, 74), (10, 37)

So, to list all the factors of 370: 1, 2, 5, 10, 37, 74, 185, 370

The negative factors of 370 would be: -1, -2, -5, -10, -37, -74, -185, -370

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 370, we break it down step by step until only prime factors remain. Then, we express 370 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 370 only has a few differences from the above method of finding the factors of 370. 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 370:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 370. 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 370 by the smallest prime factor, in this case, 2

370 ÷ 2 = 185

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 185 as the new focus. Find the smallest prime factor that isn’t 1, and divide 185 by that number. The smallest prime factor you pick for 185 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 370 are: 2, 5, 37

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

Factors of 21 - The factors of 21 are 1, 3, 7, 21

Factors of 18 - The factors of 18 are 1, 2, 3, 6, 9, 18

Factors of 117 - The factors of 117 are 1, 3, 9, 13, 39, 117

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