Math Tutor Explains: What are the Factors of 9600?

As your math tutor, I’m here to guide you through the different types of factors of 9600. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 9600: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600

• Sum of Factors of 9600: 31620

• Negative Factors of 9600: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -32, -40, -48, -50, -60, -64, -75, -80, -96, -100, -120, -128, -150, -160, -192, -200, -240, -300, -320, -384, -400, -480, -600, -640, -800, -960, -1200, -1600, -1920, -2400, -3200, -4800, -9600

• Prime Factors of 9600: 2, 3, 5

• Prime Factorization of 9600: 2^7 × 3^1 × 5^2

There are two main ways a math tutor would explain how to find the factors of 9600: 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 9600 step by step!

Factor pairs of 9600 are any two numbers that, when multiplied together, equal 9600. The question to ask is “what two numbers multiplied together equal 9600?” Every factor can be paired with another factor, and multiplying the two will result in 9600.

To find the factor pairs of 9600, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 9600. 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 9600 by the smallest prime factor, in this case, 2:

9600 ÷ 2 = 4800

2 and 4800 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 4800 as the new focus. Find the smallest prime factor that isn’t 1, and divide 4800 by that number. In this case, 2 is the new smallest prime factor:

4800 ÷ 2 = 2400

Remember that this new factor pair is only for the factors of 4800, not 9600. So, to finish the factor pair for 9600, you’d multiply 2 and 2 before pairing with 2400:

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 9600:

(1, 9600), (2, 4800), (3, 3200), (4, 2400), (5, 1920), (6, 1600), (8, 1200), (10, 960), (12, 800), (15, 640), (16, 600), (20, 480), (24, 400), (25, 384), (30, 320), (32, 300), (40, 240), (48, 200), (50, 192), (60, 160), (64, 150), (75, 128), (80, 120), (96, 100)

So, to list all the factors of 9600: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600

The negative factors of 9600 would be: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -32, -40, -48, -50, -60, -64, -75, -80, -96, -100, -120, -128, -150, -160, -192, -200, -240, -300, -320, -384, -400, -480, -600, -640, -800, -960, -1200, -1600, -1920, -2400, -3200, -4800, -9600

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 9600, we break it down step by step until only prime factors remain. Then, we express 9600 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 9600 only has a few differences from the above method of finding the factors of 9600. 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 9600:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 9600. 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 9600 by the smallest prime factor, in this case, 2

9600 ÷ 2 = 4800

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 4800 as the new focus. Find the smallest prime factor that isn’t 1, and divide 4800 by that number. The smallest prime factor you pick for 4800 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 9600 are: 2, 3, 5

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

Factors of 132 - The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128

Factors of 118 - The factors of 118 are 1, 2, 59, 118

Factors of 68 - The factors of 68 are 1, 2, 4, 17, 34, 68