 # What are factors of 9?

The factors of 9 are 1,3 and 9 are . Their sum add up to 13. It has total three factors of which 9 is the biggest factor and 1 is the smallest one.

Factors of a number are those numbers, by multiplying them will get that particular number. The list include integers which can evenly divide 9 without leaving any remainder and this list include 1,3 and 9.and the pair of the factors will be (1,9) and (3,3).
The Negative factorsof 9 will be; -1,-3 and -9.
The Prime factor of 9 is 3.
The Prime factorization of 9 will be 3^2=3*3
The Addition of factors(1,3,9) gives us 13.
The thing about factors of 9 is that, Factors are exactly divisible and they leaves no any remainder behind. for example if we divide 9 by 3, it completely divides it and leaves no any remainder.

### what are prime factors?

Prime Factors are those factor which are not a composite number but prime numbers and are termed as prime factors. Here prime factor of 9 is 3.

## Summary

So factors of a number are those natural numbers which when multiply will give that specific number or when divided leaves no remainder behind. Factors of a number can be positive numbers as well as negative numbers. Here factor of 9 are 1,3 and 9,where 9 is the greatest and 1 is the smallest factor respectively. and their sum add up to 13.

## NOTE

1 and the number itself (HERE 9) are always factors of the number.

## Methods to Calculate the Factors of 9.

So a factor is a number that divides a number equally. The way to find and list all of the factors of 9 is to go through each and every number including 9 also and check which numbers results in an even quotient. Also Factors of 9 can be calculated by Two methods.
1.By Division
2.By Prime factorization

### Factorization of 9 by Division Method.

For finding the factors of 9 by using division method, divide 9 by natural numbers and see which numbers evenly divide 9 and leaves no remainder.
Steps are as follow.

• Step 1: Divide 9 by 1, 3, and 9, with 0 as a remainder.
• Step 2: When 9 is divide by the numbers like 2 or 4, it leaves a remainder, therefore they are not the factors of 9.
• Step 3: Try to divide 9 by numbers other then 1,3 and 9 and see the result

### Prime factorization

Prime numbers is just a number that has exactly two factors: itself and 1.There’s a lot of prime numbers. Here’s a list of all the prime numbers that are less than 20: 2, 3, 5, 7, 11, 13, 17 and 19. They are the one’s you will use most often. 1 isn’t on the list of prime numbers. Well, 1 is a lot like a prime number, but for some technical reasons, it’s not considered prime. prime numbers are just special numbers that you can not factor. Well, unless you use the obvious factors of 1 and the number itself.
But what’s so special about prime numbers? Why do we need to know about them? Well, prime numbers are like the building blocks of all the other whole numbers. In fact, whole numbers that are not prime are called ‘composite’ numbers because they are composed of primes. That means that you can get them by multiplying prime numbers together.
Here is a good way to see how that works. Again we will list all the prime numbers that are less than 20. And now let’s list at all the composite numbers that are less than 20. The 1st composite number is 4, and you get 4 by multiplying the primes 2 × 2, The next composite number is 6, and you get it by multiplying the primes 2 × 3 And the next composite number is 8, which you get by multiplying the primes 2 × 2 × 2. And the composite number 9 can be made by multiplying the primes 3 × 3, We could keep going like this and you would see that ALL the composite numbers are made by multiplying different combinations of prime numbers together.
And each of these combinations is called the “prime factorization” of its composite number. prime factorization is the set of prime numbers that you multiply together to get another number.
You can also use the term ‘prime factorization’ as an ACTION to describe how we find out what prime numbers and composite number is made of. use prime factorization (the action) to find the prime factorization (the set of prime factors).
Factor 12 until all the factors are prime numbers. so you can do this using ‘factor tree; factor tree is just a diagram that helps you keep track of multiple factoring steps. When you factor a number, you write the two factors below it with lines (or branches) going to them. And then, if you factor one of the factors, you do the same thing again. so let’s get started. 12 can be factored into 2 × 6, keep going until all the factors are prime numbers.

### Factors of 9 by Prime Factorization

In the prime factorization method, 9 is divided by the prime numbers and if it does not leave any remainder then stop the division. and if it leaves any remainder then continue dividing by the quotient until no remainder left. and this how, 9 can be expressed as a product of its prime factors. There is also two method to do prime factorization,
1. By the Division method
2. By Factor tree method.

#### 1.Prime Factorization by Division Method Of 9

Here 9 is divided by the smallest prime number (3) which divides 9 exactly. The quotient obtained from the division is then divided by the smallest prime number and the process continues till the quotient is equal to 1.
Explanation

• Divide 9 by the prime number 3, (9 ÷ 3 = 3)
• As 3 is the smallest prime number, it cannot be further divided.
• So, the factors of 9 are 3 and 9.
Prime factorization of 9 can be (9 = 3 × 3.)

#### 2.Prime Factorization of 9 by Factor Tree Method

In prime factors of 9 by tree method, the root of the factor tree will be 9. write a pair of factors as a branch of 9, at each branch you can split the numbers into any factors till you reach the prime factors. Here, 3 is a prime factor.so the factor tree will end up at 3.And the prime factorization of 9 will be 3 × 3.

## Summary

There are two methods to calculate the factors of 9,one by division and second by prime factorization. In division method we divide a number till no quotient left. and in prime factorization method. In prime factors of 9 by tree method, the root of the factor tree will be 9. write a pair of factors as a branch of 9, at each branch you can split the numbers into any factors till you reach the prime factors.

## What are Factors Pairs of 9?

Combination of two factors which when be multiplied together to give that specific number is called factors pairs. and for 9, the factor pairs are as below:

• 1 x 9 = 9
• 3 x 3 = 9
Just like positive numbers negative numbers are also factors of a particular number, therefore they also form factors pairs known as negative factor pairs. negative factor pairs for 9 are as below
• -1 x -9 = 9
• -3 x -3 = 9
Keep in mind that here two negative are being multiplied, we are multiplying a minus with a minus, so the result will be a positive number; minus multiply by minus gives positive.

## Tricks to find factors any number

Factors are number which when divided gives no remainder, for example to find the factor of number 6 the first number which will divide number 6 is always 1, because 1 divides all the numbers and the number will always divide itself so you can also say that the other factor will be 6 itself. now let’s start finding out the remaining factors of number 6 so what is the number which comes after 1 is 2 so does 2 completely divided number 6 yes right 2 multiply 3 is 6. so I can say that 2 is one of the factors of number 6. Now let’s go to the next number which is what we have taken 1. we have taken 2 so the next number which comes is 3 so does 3 divide the number 6 yes it divides this number completely because we know 3 into 2 gets you 6 so we can say that the next number is 3.
okay now if you want to check we can check for four and five as well but when you divide 6 by 4 you get a remainder which is 2 so that is not a factor because you want a number with which you divide six you get the remainder as zero so that is not the case with four nor is the case with five okay so in this case I can say one two three and six are the factors of number six

## Conclusion

1,3 and 9 are the factors of 9.The number 9 has a total of three factors of which 9 is the biggest factor and 1 is the smallest one, and their sum add up to 13.Factors of a number are those numbers, which when multiply will get that particular number. The way to find and list all of the factors of 9 is to go through each and every number including 9 also and check which numbers results in an even quotient. Also Factors of 9 can be calculated by Two methods.

### 1. what are negative numbers?

Negative numbers are numbers which are less then zero, on a number line they are on left side of zero. Negative numbers can be whole numbers, decimals or fractions. For example, – 2, – 3, – 4, – 5, -2/3, -5/7, -3/4, -0.5, -0.7. are some examples of negative numbers.

### 2.Are there negative pairs of 9?

Yes there are negative pairs of 9 as well. and these are -1,-3 and -9. and there multiplication yields a positive number. they are opposite of positive numbers and are used to represent the magnitude of a loss or deficiency.

### 3.what are composite numbers?

Composite numbers are positive integer that can be obtained by multiplying two positive integers. it is a positive integer that has at least one divisor except 1 and itself. Every integer is composite, prime or the unit 1, therefore composite numbers are the numbers that are not prime and not a unit. some composite numbers are as below
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99…

### 4.What are natural numbers?

Natural numbers are apart of the number system, including all the positive numbers from 1 to infinity. they are also known as counting numbers because they do not include zero and negative numbers. natural numbers include only the positive integers, but not zero, fractions, decimals, and negative numbers.
natural numbers up to 50 are as follow.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.

### 5.What are prime factors?

Prime Factors are those factor which are prime numbers and not a composite number are called prime factors. For example prime factors of 30 will be 2,3 and 5.prime factors up to 100 are as below
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97

### 6. What does addition of factors mean?

Addition means to sum or to add something, and addition of factors mean to add or to sum up the all factors of a particular number.in case of 9 its factors are 1,3 and 9;so their sum will add up to to 13.