What Are Factors Of 9? Factors of 9 are all the whole numbers that can be divided evenly by 9. It has a total of 3 factors, with 9 being the biggest. 1, 3, and 9 are all good factors of 9. The total of all the factors of 9 is 13, and they are (1, 9) and (3, 3).
About Factors of 9
The numbers that make up a number are called its factors. If you multiply those numbers, you’ll get that number. On the list are numbers like 1,3, and 9 that can be used to divide 9 evenly without leaving a remainder. The two numbers will be (1,9) and (3,3).
| Steps | Details |
|---|---|
| 1 | Negative factors for 9 are -1, -3, and -9. |
| 2 | The most important number in 9 is 3. |
| 3 | 9 can be broken down into its prime parts by 32=3*3. |
| 4 | When we add factors (1, 3, and 9), we get 13. |
The thing about factors of 9 is that they can be divided exactly, leaving no extra numbers. For example, if we divide 9 by 3, it divides it all the way through and doesn’t leave any extra.
Divide to Find the Factors of 9
By dividing 9, we can see which natural numbers exactly divide 9 and leave 0 as the remainder. These are the prime factors of 9.
| Steps | Details |
|---|---|
| Steps | |
| 1 | The answer is 0 when we divide 9 by 1, 3, and 9. |
| 2 | When you divide 9 by a number like 2 or 4, you get a number left over. |
| 3 | Divide 9 by the numbers above and look at what you get. |
Prime Factorization
In the prime factorization method, we divide 9 by prime numbers and check to see if there is no remainder. Then, we use the quotient to keep dividing. This way, the number 9 is written as the sum of its prime factors. We can use division or a “factor tree” to find the prime factors.
Two Factors
Prime numbers are just numbers that can be broken down into just two parts: the number itself and 1. There are a lot of prime numbers. Here are all the prime numbers less than 20: 2, 3, 5, 7, 11, 13, 17, and 19. They will be the ones you use the most. The number 1 isn’t a prime number.
Well, 1 is a lot like a prime number, but it’s not considered prime for technical reasons. Prime numbers are just numbers that can’t be broken down into smaller parts other than 1 and the number itself.
Well, prime numbers are like the bricks that all other whole numbers are made of. “Composite” numbers are whole numbers that are not prime. It is because they are made up of primes. It means that they can be made by multiplying together prime numbers.
How to Divide?
9 is divided by the smallest prime number that exactly divides 9. The result is then divided by the smallest or second-smallest prime number, repeated until the result is 1.
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Let’s divide 9 by 3, which is a prime number. 9 3 = 3.
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Since 3 is the smallest odd prime number that isn’t even, it can’t be split any further.
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So, the number 9 is 3 and 9.
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The prime factors of 9 are 3 and 3.
Method of a Factor Tree
We need to figure out the 9’s prime factors. So, the number 9 is at the base of our factor tree. We need to write two factors as a branch of the number 9.
Upside-Down Method for Dividing
This method is called “upside-down division” because the symbol for division is turned around. In this case, we divide 9 by 3, the smallest prime number. If the number given is an even number, we divide it by 2.
Summary
There are two ways to figure out the factors of 9. The first is to divide the number by itself, and the second is to use prime factorization. The division method splits a number into parts until there are no more parts. And in the method of prime factors. When finding the prime factors of 9 using the tree method, 9 will be at the base of the factor tree.
All Calculation
All factorization calculations are shown in the table below.
| Number | Calculation |
|---|---|
| 1 | Factors in Pairs Factor |
| 2 | Tree Primes Between Two Numbers |
| 3 | Primes Before a Number |
Solved Examples of the Factors of 9
Here are a couple of examples.
Example
Three students have 9 minutes during a competition to discuss a certain subject. There is an equal amount of time for each of them to talk. How long will each of them have?
Solution
We have 9 minutes and 3 students. To divide the time evenly between them, we need to find the factor of 9 that divides the time equally between the three students.
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Therefore we divide 9 by 3, which gives us 3.
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Since 3 is a factor of 9, multiplying 3 by 3 gives the number 9.
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So, each student will have three minutes to talk about the subject.
Example
Ross is adding up all the parts that makeup 9. Can you give him the answer?
Solution
We know 9 = 1, 3, and 9 have these parts. So, 1 + 3 + 9 = 13 is the total of all the factors.
Example
Nick and his friends were having fun with math. In the game, he had to find the things that makeup 9. What will his reply be?
Solution
9 is made up of parts. So, the factors of the number 9 are 1, 3, and 9.
What Are the Rules for How to Divide?
Divisibility means that a given integer number can be divided by a given number, or “divider.” The divisibility rule is a quick way to tell if something is divisible or not. It includes rules about factors with odd numbers and factors with even numbers. The goal of this example is to help the student guess the status of a given number without doing any math.
How to Break Down Any Number into Its Parts?
Factors are numbers that, when divided, leave no remainder. For example, to find the factor of the number 6, the first number that divides it is always 1 since 1 divides all numbers. The number will always divide itself, so you can also say that the other factor will be 6.
Now let’s start looking for the rest of the factors of 6. What comes after one is two, so does two completely divide the number six? Yes, 2 times 3 equals 6. So, I can say that 2 is one thing that makes 6 what it is.
Let’s move on to the next number, 1, which we’ve chosen. Since we’ve already taken 2, the next number is 3, so does 3 divide 6? Yes, it completely divides this number. We know that 3 divided by 2 is 6, so we can say that the next number is 3.
We can also check for four and five if you want to. Still, if you divide 6 by 4, you get a remainder of 2, so that’s not a factor because you want a number with which you can divide 6 and get a remainder of zero. That’s not the case with four or five, so I can say that 1, 2, 3, and 6 are the factors of 6.
Summary
Divisibility is the ability of a number to be divided by a given divisor. The divisibility rule says what can be divided. It uses rules about odd and even numbers. Factors are numbers that, when divided, leave no remainder. For example, the factor of 6 is 1, since 1 divides all integers.
Frequently Asked Questions - FAQs
This topic raises some very important questions.
1 - What Is the Order of the Factors of 9?
1, 3, and 9 are all factors of 9. One is always a factor. The numbers we multiply to get a certain number are called its factors.
2 - Where Do You Look for a Factor?
Set up the number whose factors you want to find, such as 24. Find two more numbers that, when added together, add up to 24. In this case, 24 is equal to 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 24. It means that 1, 2, 3, 4, 6, 8, 12, and 24 are all factors of 24.
3 - What Does This Thing Mean?
A factor is a number that can use to divide another number without leaving an extra number. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they can be divided by the product.
4 - What Is a Factor in Math?
A factor is a number that, in math, divides another number or expression evenly, meaning there is no excess amount. For example, 12 divided by 3 is exactly 4, and 12 divided by 6 is exactly 2. 1, 2, 4, and 12 are also factors of 12.
5 - Are All Prime Numbers Odd?
Another thing to remember is that every prime number except 2 is an odd number. Some examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, etc. A composite number is any number that is not prime.
6 - Is 9 a Prime No?
The number 9 is not prime. It can also be broken up into 1 and 9. Below 20, the only prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19.
7 - Is Nine an Even Number?
No, 9 is an odd number.
8 - What Is 8 as a Factor?
A factor of 8 is a number or integer that divides 8 exactly without leaving a remainder. Because 8 is an even composite number with more than two factors, it is called a “compound number.” So, factors 1, 2, 4, and 8 add up to 8.
9 - How Do You Teach a Number’s Factors?
The best way to teach students how to find factor pairs is to have them start at 1 and work their way up. Give your students a goal number and tell them to write “1x” below it. Let them write the number itself on the right side. We know that every number has at least one “factor pair” that is itself times 1.
10 - How Many Things Makeup 24?
There are eight different ways to divide 24. The numbers are 1, 2, 3, 4, 6, 8, 12, and 24. Pair factors of 24 are the numbers that, when multiplied in pairs, add up to 24.
11 - How Many Are Just Right?
A perfect number is a positive integer where the sum of its proper divisors equals the number itself. The small number is 6, a total of 1, 2, and 3. There are also 28, 496, and 8,128 that are perfect. The first time such numbers were found is lost in the past.
12 - What Is a Number That Is Not Prime?
"A prime number is usually defined as a number that can only be divided by 1 and itself. For example, 13 is prime because only 1 and 13 can be divided by it. Since it may be split into two parts by three, 6 is not a prime.
13 - Does 1 Divide Every Number?
Every number has 1 as a part of it. Except for 1, every number has at least two parts.
14 - What Is Life If There Are No Numbers?
Without numbers, life would be hard. For example, there wouldn’t be an economy, and getting around New York would be hard if you didn’t know what street your house was on. There wouldn’t be any electronics, cars, or tall buildings.
15 - Is Number 9 the Best One?
Mihailescu’s Theorem shows that 9 is the only number that has this property. Nine is a positive perfect power that is one more than another. In the decimal system, 9 is the largest number with only one digit.
Conclusion
List of numbers with 9 factors. It has 3 factors, with 9 being the biggest. 1, 3, and 9 are all good factors. In pairs, the factors of 9 are (1, 9) and (3, 3). 9-factors can be divided exactly and leave no extra pieces. When you divide 9 by 3, there are no extras.
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