# Factors of 297

Factors of 297 are 1, 3, 9, 11, 27, 33, 99, and 297

#### How to find factors of a number

 1.   Find factors of 297 using Division Method 2.   Find factors of 297 using Prime Factorization 3.   Find factors of 297 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 297

• Divide 297 by 1: 297 ÷ 1 : Remainder = 0
• Divide 297 by 3: 297 ÷ 3 : Remainder = 0
• Divide 297 by 9: 297 ÷ 9 : Remainder = 0
• Divide 297 by 11: 297 ÷ 11 : Remainder = 0
• Divide 297 by 27: 297 ÷ 27 : Remainder = 0
• Divide 297 by 33: 297 ÷ 33 : Remainder = 0
• Divide 297 by 99: 297 ÷ 99 : Remainder = 0
• Divide 297 by 297: 297 ÷ 297 : Remainder = 0

Hence, Factors of 297 are 1, 3, 9, 11, 27, 33, 99, and 297

#### 2. Steps to find factors of 297 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 297 using the division method, follow these steps:

• Step 1. Start dividing 297 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 297, which is 3. Divide 297 by 3 to obtain the quotient (99).
297 ÷ 3 = 99
• Step 3. Repeat step 1 with the obtained quotient (99).
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1

So, the prime factorization of 297 is, 297 = 3 x 3 x 3 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 297 as shown below:

So, the prime factorization of 297 is, 297 = 3 x 3 x 3 x 11.

#### 3. Find factors of 297 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 297 would be the two numbers which, when multiplied, give 297 as the result.

The following table represents the calculation of factors of 297 in pairs:

Factor Pair Pair Factorization
1 and 297 1 x 297 = 297
3 and 99 3 x 99 = 297
9 and 33 9 x 33 = 297
11 and 27 11 x 27 = 297

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 297. They are called negative pair factors.

Hence, the negative pairs of 297 would be ( -1 , -297 ) , ( -3 , -99 ) , ( -9 , -33 ) and ( -11 , -27 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be 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, 99, 297 are exact divisors of 297.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 297 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 297.

• Which is the smallest prime factor of 297?

Smallest prime factor of 297 is 3.

• Is 297 a perfect square?

No 297 is not a perfect square.

• What are five multiples of 297?

First five multiples of 297 are 594, 891, 1188, 1485, 1782.

• What is prime factorization of 297?

Prime factorization of 297 is 3 x 3 x 3 x 11.

• What are factors of 297?

Factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297.

• How do you find factors of a negative number? ( eg. -297 )?

Factors of -297 are -1, -3, -9, -11, -27, -33, -99, -297.

• Is 297 a whole number?

Yes 297 is a whole number.

• Which is greatest factor of 297?

The greatest factor of 297 is 99.

• What are the prime factors of 297?

The factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297.
Prime factors of 297 are 3, 3, 3, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 297. Can you help her?

Prime factors of 297 are 3, 3, 3, 11.
Hence, the product of prime factors of 33.

Can you help Rubel to find out the product of the even factors of 297?

Factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297.
Even factors of 297 are 0.
Hence, product of even factors of 297 is; 0 = 0.

Joy wants to calculate mean of all the factors of 297. Help him in finding the mean of 297.

Factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 297 is 1 + 3 + 9 + 11 + 27 + 33 + 99 + 297 = 480.
Hence, the mean of factors of 297 is 480 ÷ 8 = 60.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 297? Help her in writing all the factors.

Positive factors are 1, 3, 9, 11, 27, 33, 99, 297.
Negative factors are -1, -3, -9, -11, -27, -33, -99, -297.

How many factors are there for 297?

Factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297.
So there are in total 8 factors.

Joey wants to write all the prime factors of 297 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 297 are 3, 3, 3, 11.
So in exponential form it can be written as 33 x 11.

Kevin has been asked to write 7 factor(s) of 297. Can you predict the answer?

7 factor(s) of 297 are 1, 3, 9, 11, 27, 33, 99.