# Factors of 891

Factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, and 891

#### How to find factors of a number

 1.   Find factors of 891 using Division Method 2.   Find factors of 891 using Prime Factorization 3.   Find factors of 891 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 891

• Divide 891 by 1: 891 ÷ 1 : Remainder = 0
• Divide 891 by 3: 891 ÷ 3 : Remainder = 0
• Divide 891 by 9: 891 ÷ 9 : Remainder = 0
• Divide 891 by 11: 891 ÷ 11 : Remainder = 0
• Divide 891 by 27: 891 ÷ 27 : Remainder = 0
• Divide 891 by 33: 891 ÷ 33 : Remainder = 0
• Divide 891 by 81: 891 ÷ 81 : Remainder = 0
• Divide 891 by 99: 891 ÷ 99 : Remainder = 0
• Divide 891 by 297: 891 ÷ 297 : Remainder = 0
• Divide 891 by 891: 891 ÷ 891 : Remainder = 0

Hence, Factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, and 891

#### 2. Steps to find factors of 891 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 891 using the division method, follow these steps:

• Step 1. Start dividing 891 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 891, which is 3. Divide 891 by 3 to obtain the quotient (297).
891 ÷ 3 = 297
• Step 3. Repeat step 1 with the obtained quotient (297).
297 ÷ 3 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1

So, the prime factorization of 891 is, 891 = 3 x 3 x 3 x 3 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 891 as shown below:

So, the prime factorization of 891 is, 891 = 3 x 3 x 3 x 3 x 11.

#### 3. Find factors of 891 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 891 would be the two numbers which, when multiplied, give 891 as the result.

The following table represents the calculation of factors of 891 in pairs:

Factor Pair Pair Factorization
1 and 891 1 x 891 = 891
3 and 297 3 x 297 = 891
9 and 99 9 x 99 = 891
11 and 81 11 x 81 = 891
27 and 33 27 x 33 = 891

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 891. They are called negative pair factors.

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

#### 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 number is a factor of zero (0), since 891 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 11, 27, 33, 81, 99, 297, 891 are exact divisors of 891.
• Factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891. Each factor divides 891 without leaving a remainder.

• Which is the smallest prime factor of 891?

Smallest prime factor of 891 is 3.

• Is 891 a perfect square?

No 891 is not a perfect square.

• What are five multiples of 891?

First five multiples of 891 are 1782, 2673, 3564, 4455, 5346.

• What is prime factorization of 891?

Prime factorization of 891 is 3 x 3 x 3 x 3 x 11.

• What are factors of 891?

Factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891.

• How do you find factors of a negative number? ( eg. -891 )?

Factors of -891 are -1, -3, -9, -11, -27, -33, -81, -99, -297, -891.

• Is 891 a whole number?

Yes 891 is a whole number.

• Which is greatest factor of 891?

The greatest factor of 891 is 297.

• What are the prime factors of 891?

The factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891.
Prime factors of 891 are 3, 3, 3, 3, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 891. Can you help her?

Prime factors of 891 are 3, 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 891?

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

Joy wants to calculate mean of all the factors of 891. Help him in finding the mean of 891.

Factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 891 is 1 + 3 + 9 + 11 + 27 + 33 + 81 + 99 + 297 + 891 = 1452.
Hence, the mean of factors of 891 is 1452 ÷ 10 = 145.20.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 891? Help her in writing all the factors.

Positive factors are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891.
Negative factors are -1, -3, -9, -11, -27, -33, -81, -99, -297, -891.

How many factors are there for 891?

Factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891.
So there are in total 10 factors.

Joey wants to write all the prime factors of 891 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 891 are 3, 3, 3, 3, 11.
So in exponential form it can be written as 34 x 11.

Kevin has been asked to write 9 factor(s) of 891. Can you predict the answer?

9 factor(s) of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297.