Math Tutor Explains: What are the Factors of 425?

As your math tutor, I’m here to guide you through the different types of factors of 425. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 425: 1, 5, 17, 25, 85, 425

• Sum of Factors of 425: 558

• Negative Factors of 425: -1, -5, -17, -25, -85, -425

• Prime Factors of 425: 5, 17

• Prime Factorization of 425: 5^2 × 17^1

There are two main ways a math tutor would explain how to find the factors of 425: 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 425 step by step!

Factor pairs of 425 are any two numbers that, when multiplied together, equal 425. The question to ask is “what two numbers multiplied together equal 425?” Every factor can be paired with another factor, and multiplying the two will result in 425.

To find the factor pairs of 425, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 425. 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 5.

Step 2:

Divide 425 by the smallest prime factor, in this case, 5:

425 ÷ 5 = 85

5 and 85 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 85 as the new focus. Find the smallest prime factor that isn’t 1, and divide 85 by that number. In this case, 5 is the new smallest prime factor:

85 ÷ 5 = 17

Remember that this new factor pair is only for the factors of 85, not 425. So, to finish the factor pair for 425, you’d multiply 5 and 5 before pairing with 17:

5 x 5 = 25

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 425:

(1, 425), (5, 85), (17, 25)

So, to list all the factors of 425: 1, 5, 17, 25, 85, 425

The negative factors of 425 would be: -1, -5, -17, -25, -85, -425

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 425, we break it down step by step until only prime factors remain. Then, we express 425 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 425 only has a few differences from the above method of finding the factors of 425. 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 425:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 425. 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 5.

Step 2:

Divide 425 by the smallest prime factor, in this case, 5

425 ÷ 5 = 85

5 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 85 as the new focus. Find the smallest prime factor that isn’t 1, and divide 85 by that number. The smallest prime factor you pick for 85 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 425 are: 5, 17

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

Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Factors of 125 - The factors of 125 are 1, 5, 25, 125

Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70

Factors of 111 - The factors of 111 are 1, 3, 37, 111