# Factors of 9801

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, and 9801

#### How to find factors of a number

 1.   Find factors of 9801 using Division Method 2.   Find factors of 9801 using Prime Factorization 3.   Find factors of 9801 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 9801

• Divide 9801 by 1: 9801 ÷ 1 : Remainder = 0
• Divide 9801 by 3: 9801 ÷ 3 : Remainder = 0
• Divide 9801 by 9: 9801 ÷ 9 : Remainder = 0
• Divide 9801 by 11: 9801 ÷ 11 : Remainder = 0
• Divide 9801 by 27: 9801 ÷ 27 : Remainder = 0
• Divide 9801 by 33: 9801 ÷ 33 : Remainder = 0
• Divide 9801 by 81: 9801 ÷ 81 : Remainder = 0
• Divide 9801 by 99: 9801 ÷ 99 : Remainder = 0
• Divide 9801 by 121: 9801 ÷ 121 : Remainder = 0
• Divide 9801 by 297: 9801 ÷ 297 : Remainder = 0
• Divide 9801 by 363: 9801 ÷ 363 : Remainder = 0
• Divide 9801 by 891: 9801 ÷ 891 : Remainder = 0
• Divide 9801 by 1089: 9801 ÷ 1089 : Remainder = 0
• Divide 9801 by 3267: 9801 ÷ 3267 : Remainder = 0
• Divide 9801 by 9801: 9801 ÷ 9801 : Remainder = 0

Hence, Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, and 9801

#### 2. Steps to find factors of 9801 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 9801 using the division method, follow these steps:

• Step 1. Start dividing 9801 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 9801, which is 3. Divide 9801 by 3 to obtain the quotient (3267).
9801 ÷ 3 = 3267
• Step 3. Repeat step 1 with the obtained quotient (3267).
3267 ÷ 3 = 1089
1089 ÷ 3 = 363
363 ÷ 3 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1

So, the prime factorization of 9801 is, 9801 = 3 x 3 x 3 x 3 x 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 9801 as shown below:

So, the prime factorization of 9801 is, 9801 = 3 x 3 x 3 x 3 x 11 x 11.

#### 3. Find factors of 9801 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 9801 would be the two numbers which, when multiplied, give 9801 as the result.

The following table represents the calculation of factors of 9801 in pairs:

Factor Pair Pair Factorization
1 and 9801 1 x 9801 = 9801
3 and 3267 3 x 3267 = 9801
9 and 1089 9 x 1089 = 9801
11 and 891 11 x 891 = 9801
27 and 363 27 x 363 = 9801
33 and 297 33 x 297 = 9801
81 and 121 81 x 121 = 9801
99 and 99 99 x 99 = 9801

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 9801. They are called negative pair factors.

Hence, the negative pairs of 9801 would be ( -1 , -9801 ) , ( -3 , -3267 ) , ( -9 , -1089 ) , ( -11 , -891 ) , ( -27 , -363 ) , ( -33 , -297 ) , ( -81 , -121 ) and ( -99 , -99 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801 are exact divisors of 9801.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 9801 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 9801.

• Which is the smallest prime factor of 9801?

Smallest prime factor of 9801 is 3.

• Is 9801 a perfect square?

Yes 9801 is a perfect square.

• What are five multiples of 9801?

First five multiples of 9801 are 19602, 29403, 39204, 49005, 58806.

• What is prime factorization of 9801?

Prime factorization of 9801 is 3 x 3 x 3 x 3 x 11 x 11.

• What are factors of 9801?

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.

• How do you find factors of a negative number? ( eg. -9801 )?

Factors of -9801 are -1, -3, -9, -11, -27, -33, -81, -99, -121, -297, -363, -891, -1089, -3267, -9801.

• Is 9801 a whole number?

Yes 9801 is a whole number.

• Which is greatest factor of 9801?

The greatest factor of 9801 is 3267.

• What are the prime factors of 9801?

The factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
Prime factors of 9801 are 3, 3, 3, 3, 11, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 9801. Can you help her?

Prime factors of 9801 are 3, 3, 3, 3, 11, 11.
Hence, the product of prime factors of 33.

Can you help Rubel to find out the product of the even factors of 9801?

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
Even factors of 9801 are 0.
Hence, product of even factors of 9801 is; 0 = 0.

Joy wants to calculate mean of all the factors of 9801. Help him in finding the mean of 9801.

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 9801 is 1 + 3 + 9 + 11 + 27 + 33 + 81 + 99 + 121 + 297 + 363 + 891 + 1089 + 3267 + 9801 = 16093.
Hence, the mean of factors of 9801 is 16093 ÷ 15 = 1072.87.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 9801? Help her in writing all the factors.

Positive factors are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
Negative factors are -1, -3, -9, -11, -27, -33, -81, -99, -121, -297, -363, -891, -1089, -3267, -9801.

How many factors are there for 9801?

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
So there are in total 15 factors.

Joey wants to write all the prime factors of 9801 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 9801 are 3, 3, 3, 3, 11, 11.
So in exponential form it can be written as 34 x 112.

Kevin has been asked to write 14 factor(s) of 9801. Can you predict the answer?

14 factor(s) of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267.