# Factors of 261

Factors of 261 are 1, 3, 9, 29, 87, and 261

#### How to find factors of a number

 1.   Find factors of 261 using Division Method 2.   Find factors of 261 using Prime Factorization 3.   Find factors of 261 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 261

• Divide 261 by 1: 261 ÷ 1 : Remainder = 0
• Divide 261 by 3: 261 ÷ 3 : Remainder = 0
• Divide 261 by 9: 261 ÷ 9 : Remainder = 0
• Divide 261 by 29: 261 ÷ 29 : Remainder = 0
• Divide 261 by 87: 261 ÷ 87 : Remainder = 0
• Divide 261 by 261: 261 ÷ 261 : Remainder = 0

Hence, Factors of 261 are 1, 3, 9, 29, 87, and 261

#### 2. Steps to find factors of 261 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 261 using the division method, follow these steps:

• Step 1. Start dividing 261 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 261, which is 3. Divide 261 by 3 to obtain the quotient (87).
261 ÷ 3 = 87
• Step 3. Repeat step 1 with the obtained quotient (87).
87 ÷ 3 = 29
29 ÷ 29 = 1

So, the prime factorization of 261 is, 261 = 3 x 3 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 261 as shown below:

So, the prime factorization of 261 is, 261 = 3 x 3 x 29.

#### 3. Find factors of 261 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 261 would be the two numbers which, when multiplied, give 261 as the result.

The following table represents the calculation of factors of 261 in pairs:

Factor Pair Pair Factorization
1 and 261 1 x 261 = 261
3 and 87 3 x 87 = 261
9 and 29 9 x 29 = 261

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 261. They are called negative pair factors.

Hence, the negative pairs of 261 would be ( -1 , -261 ) , ( -3 , -87 ) and ( -9 , -29 ) .

#### 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, 29, 87, 261 are exact divisors of 261.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 261 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 261.

• Which is the smallest prime factor of 261?

Smallest prime factor of 261 is 3.

• Is 261 a perfect square?

No 261 is not a perfect square.

• What are five multiples of 261?

First five multiples of 261 are 522, 783, 1044, 1305, 1566.

• What is prime factorization of 261?

Prime factorization of 261 is 3 x 3 x 29.

• What are factors of 261?

Factors of 261 are 1, 3, 9, 29, 87, 261.

• How do you find factors of a negative number? ( eg. -261 )?

Factors of -261 are -1, -3, -9, -29, -87, -261.

• Is 261 a whole number?

Yes 261 is a whole number.

• Which is greatest factor of 261?

The greatest factor of 261 is 87.

• What are the prime factors of 261?

The factors of 261 are 1, 3, 9, 29, 87, 261.
Prime factors of 261 are 3, 3, 29.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 261. Can you help her?

Prime factors of 261 are 3, 3, 29.
Hence, the product of prime factors of 87.

Can you help Rubel to find out the product of the even factors of 261?

Factors of 261 are 1, 3, 9, 29, 87, 261.
Even factors of 261 are 0.
Hence, product of even factors of 261 is; 0 = 0.

Joy wants to calculate mean of all the factors of 261. Help him in finding the mean of 261.

Factors of 261 are 1, 3, 9, 29, 87, 261.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 261 is 1 + 3 + 9 + 29 + 87 + 261 = 390.
Hence, the mean of factors of 261 is 390 ÷ 6 = 65.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 261? Help her in writing all the factors.

Positive factors are 1, 3, 9, 29, 87, 261.
Negative factors are -1, -3, -9, -29, -87, -261.

How many factors are there for 261?

Factors of 261 are 1, 3, 9, 29, 87, 261.
So there are in total 6 factors.

Joey wants to write all the prime factors of 261 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 261 are 3, 3, 29.
So in exponential form it can be written as 32 x 29.

Kevin has been asked to write 5 factor(s) of 261. Can you predict the answer?

5 factor(s) of 261 are 1, 3, 9, 29, 87.