# Factors of 116

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

#### How to find factors of a number

 1.   Find factors of 116 using Division Method 2.   Find factors of 116 using Prime Factorization 3.   Find factors of 116 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 116

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

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

#### 2. Steps to find factors of 116 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 116 using the division method, follow these steps:

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

So, the prime factorization of 116 is, 116 = 2 x 2 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 116 as shown below:

So, the prime factorization of 116 is, 116 = 2 x 2 x 29.

#### 3. Find factors of 116 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 116 would be the two numbers which, when multiplied, give 116 as the result.

The following table represents the calculation of factors of 116 in pairs:

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

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 116. They are called negative pair factors.

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

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

• What is prime factorization of 116?

Prime factorization of 116 is 2 x 2 x 29.

• How do you find factors of a negative number? ( eg. -116 )?

Factors of -116 are -1, -2, -4, -29, -58, -116.

• What are the prime factors of 116?

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

• What are pair factors of 116?

The pair factors of 116 are (1,116), (2,58), (4,29).

• What is the greatest prime factors of 116?

The greatest prime factor of 116 is 29.

• What are six multiples of 116?

First five multiples of 116 are 232, 348, 464, 580, 696, 812.

• What are factors of 116?

Factors of 116 are 1, 2, 4, 29, 58, 116.

• Which is the smallest prime factor of 116?

Smallest prime factor of 116 is 2.

• Is 116 a whole number?

Yes 116 is a whole number.

#### Examples of Factors

Kevin has been asked to write 5 factor(s) of 116. Can you predict the answer?

5 factor(s) of 116 are 1, 2, 4, 29, 58.

Sammy is puzzled while calculating the prime factors of 116. Can you help him find them?

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

What is prime factorization of 116?

Prime factorization of 116 is 2 x 2 x 29 = 22 x 29.

Ariel has been assigned the task to find the product of all the prime factors of 116. Can you help her?

Prime factors of 116 are 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 116?

Factors of 116 are 1, 2, 4, 29, 58, 116.
Even factors of 116 are 2, 4, 58, 116.
Hence, product of even factors of 116 is; 2 x 4 x 58 x 116 = 53824.

Joy wants to calculate mean of all the factors of 116. Help him in finding the mean of 116.

Factors of 116 are 1, 2, 4, 29, 58, 116.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 116 is 1 + 2 + 4 + 29 + 58 + 116 = 210.
Hence, the mean of factors of 116 is 210 ÷ 6 = 35.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 116? Help her in writing all the factors.

Positive factors are 1, 2, 4, 29, 58, 116.
Negative factors are -1, -2, -4, -29, -58, -116.