# Factors of 232

Factors of 232 are 1, 2, 4, 8, 29, 58, 116, and 232

#### How to find factors of a number

 1.   Find factors of 232 using Division Method 2.   Find factors of 232 using Prime Factorization 3.   Find factors of 232 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 232

• Divide 232 by 1: 232 ÷ 1 : Remainder = 0
• Divide 232 by 2: 232 ÷ 2 : Remainder = 0
• Divide 232 by 4: 232 ÷ 4 : Remainder = 0
• Divide 232 by 8: 232 ÷ 8 : Remainder = 0
• Divide 232 by 29: 232 ÷ 29 : Remainder = 0
• Divide 232 by 58: 232 ÷ 58 : Remainder = 0
• Divide 232 by 116: 232 ÷ 116 : Remainder = 0
• Divide 232 by 232: 232 ÷ 232 : Remainder = 0

Hence, Factors of 232 are 1, 2, 4, 8, 29, 58, 116, and 232

#### 2. Steps to find factors of 232 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 232 using the division method, follow these steps:

• Step 1. Start dividing 232 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 232, which is 2. Divide 232 by 2 to obtain the quotient (116).
232 ÷ 2 = 116
• Step 3. Repeat step 1 with the obtained quotient (116).
116 ÷ 2 = 58
58 ÷ 2 = 29
29 ÷ 29 = 1

So, the prime factorization of 232 is, 232 = 2 x 2 x 2 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 232 as shown below:

So, the prime factorization of 232 is, 232 = 2 x 2 x 2 x 29.

#### 3. Find factors of 232 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 232 would be the two numbers which, when multiplied, give 232 as the result.

The following table represents the calculation of factors of 232 in pairs:

Factor Pair Pair Factorization
1 and 232 1 x 232 = 232
2 and 116 2 x 116 = 232
4 and 58 4 x 58 = 232
8 and 29 8 x 29 = 232

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 232. They are called negative pair factors.

Hence, the negative pairs of 232 would be ( -1 , -232 ) , ( -2 , -116 ) , ( -4 , -58 ) and ( -8 , -29 ) .

#### 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

• Each number is a factor of itself. Eg. 232 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 232.
• Every number is a factor of zero (0), since 232 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, 2, 4, 8, 29, 58, 116, 232 are exact divisors of 232.
• Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. Each factor divides 232 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 29, 58, 116, 232 are all less than or equal to 232.

• Which is the smallest prime factor of 232?

The smallest prime factor of 232 is 2.

• Is 232 a whole number?

Yes 232 is a whole number.

• What are the prime factors of 232?

The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232.
Prime factors of 232 are 2, 2, 2, 29.

• What two numbers make 232?

Two numbers that make 232 are 2 and 116.

• What are multiples of 232?

First five multiples of 232 are 464, 696, 928, 1160.

• What is the sum of all factors of 232?

The sum of all factors of 232 is 450.

• What are five multiples of 232?

First five multiples of 232 are 464, 696, 928, 1160, 1392.

• Is 232 a perfect square?

No 232 is not a perfect square.

• What is the greatest prime factors of 232?

The greatest prime factor of 232 is 29.

#### Examples of Factors

How many factors are there for 232?

Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 232. Can you predict the answer?

7 factor(s) of 232 are 1, 2, 4, 8, 29, 58, 116.

Sammy is puzzled while calculating the prime factors of 232. Can you help him find them?

Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232.
Prime factors of 232 are 2, 2, 2, 29

What is prime factorization of 232?

Prime factorization of 232 is 2 x 2 x 2 x 29 = 23 x 29.

Ariel has been assigned the task to find the product of all the prime factors of 232. Can you help her?

Prime factors of 232 are 2, 2, 2, 29.
Hence, the product of prime factors of 58.

Can you help Rubel to find out the product of the even factors of 232?

Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232.
Even factors of 232 are 2, 4, 8, 58, 116, 232.
Hence, product of even factors of 232 is; 2 x 4 x 8 x 58 x 116 x 232 = 99897344.

Joy wants to calculate mean of all the factors of 232. Help him in finding the mean of 232.

Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 232 is 1 + 2 + 4 + 8 + 29 + 58 + 116 + 232 = 450.
Hence, the mean of factors of 232 is 450 ÷ 8 = 56.25.