Factors of 9
by Lily, Aug 07 2023
What Are Factors of 9?
Picture this: factors of a number are those special whole numbers that can divide the number evenly, without leaving any leftovers! For the number 9, its factors are those friendly numbers that can perfectly fit into 9! So, what are the factors of 9? Let's find out!
Factors of 9
The number 9 has three magical factors: 1, 3, and 9! Isn't that fascinating? Let's see how these factors work their magic!
- 1 x 9 = 9
- 3 x 3 = 9
Voila! These factors, 1, 3, and 9, work together to create the number 9! Additionally, we know that the product of two negative numbers is only a positive number. Therefore, the factors for the number 9 are 1, -1, 3, -3, 9, and -9.
Sum of Factors
Here's a cool math trick! Did you know that the sum of all the factors of 9 is also magical? Let's add them up and see what we get!
1 + 3 + 9 = 13
Wow! The sum of all the factors of 9 is 13! How amazing is that?
Finding Factors of 9
Now, let's learn how to find the factors of 9 using the division method and the prime factorization method! Are you ready? Let's go!
- Division Method
We'll start with the division method. To find the factors of 9, we'll divide 9 by different numbers and see which ones give us whole numbers with no remainders! Let's try it!
- 9 ÷ 1 = 9 (Perfect fit! Factor: 1)
- 9 ÷ 2 = 4.5 (Nope, not a whole number!)
- 9 ÷ 3 = 3 (Perfect fit! Factor: 3)
- 9 ÷ 4 = 2.25 (Nope, not a whole number!)
- 9 ÷ 5 = 1.8 (Nope, not a whole number!)
- 9 ÷ 6 = 1.5 (Nope, not a whole number!)
- 9 ÷ 7 = 1.2857 (Nope, not a whole number!)
- 9 ÷ 8 = 1.125 (Nope, not a whole number!)
- 9 ÷ 9 = 1 (Perfect fit! Factor: 9)
There you have it! The factors of 9 are 1, 3, and 9, just as we discovered before!
- Prime Factorization Method
Next, let's explore the prime factorization method! We'll find the prime factors of 9 by breaking it down into its magical prime components. Here's how it works!
- Step 1: Start with the number 9.
- Step 2: Find the smallest prime factor. In this case, it's 3.
- Step 3: Divide 9 by 3.
9 ÷ 3 = 3
- Step 4: Keep going until you get 1.
3 ÷ 3 = 1
- Step 5: The prime factors are 3 and 3.
Fun Fact
Did you know that the prime factors of a number are like its unique DNA? They can't be broken down any further, just like how 9 is made up of the prime factors 3 and 3!
Conclusion
Factors are like friends of a number that can divide it evenly. The factors of 9 are 1, 3, and 9. Prime factorization helps us find the smallest friends that can only divide by themselves and one, which is 3 × 3 for 9. Have fun exploring the beautiful world of numbers!