# Factors of 114

Factors of 114 are 1, 2, 3, 6, 19, 38, 57, and 114

#### How to find factors of a number

 1.   Find factors of 114 using Division Method 2.   Find factors of 114 using Prime Factorization 3.   Find factors of 114 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 114

• Divide 114 by 1: 114 ÷ 1 : Remainder = 0
• Divide 114 by 2: 114 ÷ 2 : Remainder = 0
• Divide 114 by 3: 114 ÷ 3 : Remainder = 0
• Divide 114 by 6: 114 ÷ 6 : Remainder = 0
• Divide 114 by 19: 114 ÷ 19 : Remainder = 0
• Divide 114 by 38: 114 ÷ 38 : Remainder = 0
• Divide 114 by 57: 114 ÷ 57 : Remainder = 0
• Divide 114 by 114: 114 ÷ 114 : Remainder = 0

Hence, Factors of 114 are 1, 2, 3, 6, 19, 38, 57, and 114

#### 2. Steps to find factors of 114 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 114 using the division method, follow these steps:

• Step 1. Start dividing 114 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 114, which is 2. Divide 114 by 2 to obtain the quotient (57).
114 ÷ 2 = 57
• Step 3. Repeat step 1 with the obtained quotient (57).
57 ÷ 3 = 19
19 ÷ 19 = 1

So, the prime factorization of 114 is, 114 = 2 x 3 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 114 as shown below:

So, the prime factorization of 114 is, 114 = 2 x 3 x 19.

#### 3. Find factors of 114 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 114 would be the two numbers which, when multiplied, give 114 as the result.

The following table represents the calculation of factors of 114 in pairs:

Factor Pair Pair Factorization
1 and 114 1 x 114 = 114
2 and 57 2 x 57 = 114
3 and 38 3 x 38 = 114
6 and 19 6 x 19 = 114

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 114. They are called negative pair factors.

Hence, the negative pairs of 114 would be ( -1 , -114 ) , ( -2 , -57 ) , ( -3 , -38 ) and ( -6 , -19 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 114 is a factor of itself.
• 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, 3, 6, 19, 38, 57, 114 are exact divisors of 114.
• 1 is a factor of every number. Eg. 1 is a factor of 114.
• Every number is a factor of zero (0), since 114 x 0 = 0.

• How do you find factors of a negative number? ( eg. -114 )?

Factors of -114 are -1, -2, -3, -6, -19, -38, -57, -114.

• What is the sum of all factors of 114?

The sum of all factors of 114 is 240.

• What is prime factorization of 114?

Prime factorization of 114 is 2 x 3 x 19.

• What are the pair factors of 114?

Pair factors of 114 are (1,114), (2,57), (3,38), (6,19).

• What are six multiples of 114?

First five multiples of 114 are 228, 342, 456, 570, 684, 798.

• Is 114 a whole number?

Yes 114 is a whole number.

• Which is the smallest prime factor of 114?

Smallest prime factor of 114 is 2.

• What are five multiples of 114?

First five multiples of 114 are 228, 342, 456, 570, 684.

• Write all factors of 114?

Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114.

#### Examples of Factors

Joey wants to write all the prime factors of 114 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 114 are 2, 3, 19.
So in exponential form it can be written as 2 x 3 x 19.

How many factors are there for 114?

Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 114. Can you predict the answer?

7 factor(s) of 114 are 1, 2, 3, 6, 19, 38, 57.

Sammy is puzzled while calculating the prime factors of 114. Can you help him find them?

Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114.
Prime factors of 114 are 2, 3, 19

What is prime factorization of 114?

Prime factorization of 114 is 2 x 3 x 19 = 2 x 3 x 19.

Ariel has been assigned the task to find the product of all the prime factors of 114. Can you help her?

Prime factors of 114 are 2, 3, 19.
Hence, the product of prime factors of 114.

Can you help Rubel to find out the product of the even factors of 114?

Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114.
Even factors of 114 are 2, 6, 38, 114.
Hence, product of even factors of 114 is; 2 x 6 x 38 x 114 = 51984.