# Factors of 296

Factors of 296 are 1, 2, 4, 8, 37, 74, 148, and 296

#### How to find factors of a number

 1.   Find factors of 296 using Division Method 2.   Find factors of 296 using Prime Factorization 3.   Find factors of 296 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 296

• Divide 296 by 1: 296 ÷ 1 : Remainder = 0
• Divide 296 by 2: 296 ÷ 2 : Remainder = 0
• Divide 296 by 4: 296 ÷ 4 : Remainder = 0
• Divide 296 by 8: 296 ÷ 8 : Remainder = 0
• Divide 296 by 37: 296 ÷ 37 : Remainder = 0
• Divide 296 by 74: 296 ÷ 74 : Remainder = 0
• Divide 296 by 148: 296 ÷ 148 : Remainder = 0
• Divide 296 by 296: 296 ÷ 296 : Remainder = 0

Hence, Factors of 296 are 1, 2, 4, 8, 37, 74, 148, and 296

#### 2. Steps to find factors of 296 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 296 using the division method, follow these steps:

• Step 1. Start dividing 296 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 296, which is 2. Divide 296 by 2 to obtain the quotient (148).
296 ÷ 2 = 148
• Step 3. Repeat step 1 with the obtained quotient (148).
148 ÷ 2 = 74
74 ÷ 2 = 37
37 ÷ 37 = 1

So, the prime factorization of 296 is, 296 = 2 x 2 x 2 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 296 as shown below:

So, the prime factorization of 296 is, 296 = 2 x 2 x 2 x 37.

#### 3. Find factors of 296 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 296 would be the two numbers which, when multiplied, give 296 as the result.

The following table represents the calculation of factors of 296 in pairs:

Factor Pair Pair Factorization
1 and 296 1 x 296 = 296
2 and 148 2 x 148 = 296
4 and 74 4 x 74 = 296
8 and 37 8 x 37 = 296

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 296. They are called negative pair factors.

Hence, the negative pairs of 296 would be ( -1 , -296 ) , ( -2 , -148 ) , ( -4 , -74 ) and ( -8 , -37 ) .

#### 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

• Each number is a factor of itself. Eg. 296 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 296.
• Every number is a factor of zero (0), since 296 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, 37, 74, 148, 296 are exact divisors of 296.
• Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296. Each factor divides 296 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 37, 74, 148, 296 are all less than or equal to 296.

• What is prime factorization of 296?

Prime factorization of 296 is 2 x 2 x 2 x 37.

• How do you find factors of a negative number? ( eg. -296 )?

Factors of -296 are -1, -2, -4, -8, -37, -74, -148, -296.

• What are the prime factors of 296?

The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296.
Prime factors of 296 are 2, 2, 2, 37.

• What are pair factors of 296?

The pair factors of 296 are (1,296), (2,148), (4,74), (8,37).

• What is the greatest prime factors of 296?

The greatest prime factor of 296 is 37.

• What are six multiples of 296?

First five multiples of 296 are 592, 888, 1184, 1480, 1776, 2072.

• What are factors of 296?

Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296.

• Which is the smallest prime factor of 296?

Smallest prime factor of 296 is 2.

• Is 296 a whole number?

Yes 296 is a whole number.

#### Examples of Factors

Kevin has been asked to write 7 factor(s) of 296. Can you predict the answer?

7 factor(s) of 296 are 1, 2, 4, 8, 37, 74, 148.

Sammy is puzzled while calculating the prime factors of 296. Can you help him find them?

Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296.
Prime factors of 296 are 2, 2, 2, 37

What is prime factorization of 296?

Prime factorization of 296 is 2 x 2 x 2 x 37 = 23 x 37.

Ariel has been assigned the task to find the product of all the prime factors of 296. Can you help her?

Prime factors of 296 are 2, 2, 2, 37.
Hence, the product of prime factors of 74.

Can you help Rubel to find out the product of the even factors of 296?

Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296.
Even factors of 296 are 2, 4, 8, 74, 148, 296.
Hence, product of even factors of 296 is; 2 x 4 x 8 x 74 x 148 x 296 = 207474688.

Joy wants to calculate mean of all the factors of 296. Help him in finding the mean of 296.

Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 296 is 1 + 2 + 4 + 8 + 37 + 74 + 148 + 296 = 570.
Hence, the mean of factors of 296 is 570 ÷ 8 = 71.25.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 296? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 37, 74, 148, 296.
Negative factors are -1, -2, -4, -8, -37, -74, -148, -296.