# Factors of 14

Factors of 14 are 1, 2, 7, and 14

#### How to find factors of a number

 1.   Find factors of 14 using Division Method 2.   Find factors of 14 using Prime Factorization 3.   Find factors of 14 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 14

• Divide 14 by 1: 14 ÷ 1 : Remainder = 0
• Divide 14 by 2: 14 ÷ 2 : Remainder = 0
• Divide 14 by 7: 14 ÷ 7 : Remainder = 0
• Divide 14 by 14: 14 ÷ 14 : Remainder = 0

Hence, Factors of 14 are 1, 2, 7, and 14

#### 2. Steps to find factors of 14 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 14 using the division method, follow these steps:

• Step 1. Start dividing 14 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 14, which is 2. Divide 14 by 2 to obtain the quotient (7).
14 ÷ 2 = 7
• Step 3. Repeat step 1 with the obtained quotient (7).
7 ÷ 7 = 1

So, the prime factorization of 14 is, 14 = 2 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 14 as shown below:

So, the prime factorization of 14 is, 14 = 2 x 7.

#### 3. Find factors of 14 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 14 would be the two numbers which, when multiplied, give 14 as the result.

The following table represents the calculation of factors of 14 in pairs:

Factor Pair Pair Factorization
1 and 14 1 x 14 = 14
2 and 7 2 x 7 = 14

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 14. They are called negative pair factors.

Hence, the negative pairs of 14 would be ( -1 , -14 ) , ( -2 , -7 ) .

#### 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. 14 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, 7, 14 are exact divisors of 14.
• 1 is a factor of every number. Eg. 1 is a factor of 14.
• Every number is a factor of zero (0), since 14 x 0 = 0.

• What are the pair factors of 14?

Pair factors of 14 are (1,14), (2,7).

• What are five multiples of 14?

First five multiples of 14 are 28, 42, 56, 70, 84.

• What two numbers make 14?

Two numbers that make 14 are 2 and 7.

• What is the sum of all factors of 14?

The sum of all factors of 14 is 24.

• What are factors of -14?

Factors of -14 are -1, -2, -7, -14.

• What are factors of 14?

Factors of 14 are 1, 2, 7, 14.

• Is 14 a perfect square?

No 14 is not a perfect square.

• Which is the smallest prime factor of 14?

Smallest prime factor of 14 is 2.

• Which is greatest factor of 14?

The greatest factor of 14 is 7.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 14?

Factors of 14 are 1, 2, 7, 14.
Odd factors of 14 are 1, 7.
Hence product of odd factors of 14 is; 1 x 7 = 7.

Joey wants to write all the prime factors of 14 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 14 are 2, 7.
So in exponential form it can be written as 2 x 7.

How many factors are there for 14?

Factors of 14 are 1, 2, 7, 14.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 14. Can you predict the answer?

3 factor(s) of 14 are 1, 2, 7.

Sammy is puzzled while calculating the prime factors of 14. Can you help him find them?

Factors of 14 are 1, 2, 7, 14.
Prime factors of 14 are 2, 7

What is prime factorization of 14?

Prime factorization of 14 is 2 x 7 = 2 x 7.

Can you help Rubel to find out the product of the even factors of 14?

Factors of 14 are 1, 2, 7, 14.
Even factors of 14 are 2, 14.
Hence, product of even factors of 14 is; 2 x 14 = 28.