Math Tutor Explains: What are the Factors of 5625?

As your math tutor, I’m here to guide you through the different types of factors of 5625. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 5625: 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625

• Sum of Factors of 5625: 10153

• Negative Factors of 5625: -1, -3, -5, -9, -15, -25, -45, -75, -125, -225, -375, -625, -1125, -1875, -5625

• Prime Factors of 5625: 3, 5

• Prime Factorization of 5625: 3^2 × 5^4

There are two main ways a math tutor would explain how to find the factors of 5625: 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 5625 step by step!

Factor pairs of 5625 are any two numbers that, when multiplied together, equal 5625. The question to ask is “what two numbers multiplied together equal 5625?” Every factor can be paired with another factor, and multiplying the two will result in 5625.

To find the factor pairs of 5625, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 5625. 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 3.

Step 2:

Divide 5625 by the smallest prime factor, in this case, 3:

5625 ÷ 3 = 1875

3 and 1875 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 1875 as the new focus. Find the smallest prime factor that isn’t 1, and divide 1875 by that number. In this case, 3 is the new smallest prime factor:

1875 ÷ 3 = 625

Remember that this new factor pair is only for the factors of 1875, not 5625. So, to finish the factor pair for 5625, you’d multiply 3 and 3 before pairing with 625:

3 x 3 = 9

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 5625:

(1, 5625), (3, 1875), (5, 1125), (9, 625), (15, 375), (25, 225), (45, 125), (75, 75)

So, to list all the factors of 5625: 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625

The negative factors of 5625 would be: -1, -3, -5, -9, -15, -25, -45, -75, -125, -225, -375, -625, -1125, -1875, -5625

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 5625, we break it down step by step until only prime factors remain. Then, we express 5625 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 5625 only has a few differences from the above method of finding the factors of 5625. 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 5625:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 5625. 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 3.

Step 2:

Divide 5625 by the smallest prime factor, in this case, 3

5625 ÷ 3 = 1875

3 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 1875 as the new focus. Find the smallest prime factor that isn’t 1, and divide 1875 by that number. The smallest prime factor you pick for 1875 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 5625 are: 3, 5

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

Factors of 138 - The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138

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

Factors of 81 - The factors of 81 are 1, 3, 9, 27, 81

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