# Factors of 231

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, and 231

#### How to find factors of a number

 1.   Find factors of 231 using Division Method 2.   Find factors of 231 using Prime Factorization 3.   Find factors of 231 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 231

• Divide 231 by 1: 231 ÷ 1 : Remainder = 0
• Divide 231 by 3: 231 ÷ 3 : Remainder = 0
• Divide 231 by 7: 231 ÷ 7 : Remainder = 0
• Divide 231 by 11: 231 ÷ 11 : Remainder = 0
• Divide 231 by 21: 231 ÷ 21 : Remainder = 0
• Divide 231 by 33: 231 ÷ 33 : Remainder = 0
• Divide 231 by 77: 231 ÷ 77 : Remainder = 0
• Divide 231 by 231: 231 ÷ 231 : Remainder = 0

Hence, Factors of 231 are 1, 3, 7, 11, 21, 33, 77, and 231

#### 2. Steps to find factors of 231 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 231 using the division method, follow these steps:

• Step 1. Start dividing 231 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 231, which is 3. Divide 231 by 3 to obtain the quotient (77).
231 ÷ 3 = 77
• Step 3. Repeat step 1 with the obtained quotient (77).
77 ÷ 7 = 11
11 ÷ 11 = 1

So, the prime factorization of 231 is, 231 = 3 x 7 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 231 as shown below:

So, the prime factorization of 231 is, 231 = 3 x 7 x 11.

#### 3. Find factors of 231 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 231 would be the two numbers which, when multiplied, give 231 as the result.

The following table represents the calculation of factors of 231 in pairs:

Factor Pair Pair Factorization
1 and 231 1 x 231 = 231
3 and 77 3 x 77 = 231
7 and 33 7 x 33 = 231
11 and 21 11 x 21 = 231

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 231. They are called negative pair factors.

Hence, the negative pairs of 231 would be ( -1 , -231 ) , ( -3 , -77 ) , ( -7 , -33 ) and ( -11 , -21 ) .

#### 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 231 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, 7, 11, 21, 33, 77, 231 are exact divisors of 231.
• Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. Each factor divides 231 without leaving a remainder.

• How do you find factors of a negative number? ( eg. -231 )?

Factors of -231 are -1, -3, -7, -11, -21, -33, -77, -231.

• What is the sum of all factors of 231?

The sum of all factors of 231 is 384.

• What is prime factorization of 231?

Prime factorization of 231 is 3 x 7 x 11.

• What are the pair factors of 231?

Pair factors of 231 are (1,231), (3,77), (7,33), (11,21).

• What are six multiples of 231?

First five multiples of 231 are 462, 693, 924, 1155, 1386, 1617.

• Is 231 a whole number?

Yes 231 is a whole number.

• Which is the smallest prime factor of 231?

Smallest prime factor of 231 is 3.

• What are five multiples of 231?

First five multiples of 231 are 462, 693, 924, 1155, 1386.

• Write all factors of 231?

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.

#### Examples of Factors

Joey wants to write all the prime factors of 231 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 231 are 3, 7, 11.
So in exponential form it can be written as 3 x 7 x 11.

How many factors are there for 231?

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 231. Can you predict the answer?

7 factor(s) of 231 are 1, 3, 7, 11, 21, 33, 77.

Sammy is puzzled while calculating the prime factors of 231. Can you help him find them?

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.
Prime factors of 231 are 3, 7, 11

What is prime factorization of 231?

Prime factorization of 231 is 3 x 7 x 11 = 3 x 7 x 11.

Ariel has been assigned the task to find the product of all the prime factors of 231. Can you help her?

Prime factors of 231 are 3, 7, 11.
Hence, the product of prime factors of 231.

Can you help Rubel to find out the product of the even factors of 231?

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.
Even factors of 231 are 0.
Hence, product of even factors of 231 is; 0 = 0.