# Factors of 168

Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168

#### How to find factors of a number

 1.   Find factors of 168 using Division Method 2.   Find factors of 168 using Prime Factorization 3.   Find factors of 168 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 168

• Divide 168 by 1: 168 ÷ 1 : Remainder = 0
• Divide 168 by 2: 168 ÷ 2 : Remainder = 0
• Divide 168 by 3: 168 ÷ 3 : Remainder = 0
• Divide 168 by 4: 168 ÷ 4 : Remainder = 0
• Divide 168 by 6: 168 ÷ 6 : Remainder = 0
• Divide 168 by 7: 168 ÷ 7 : Remainder = 0
• Divide 168 by 8: 168 ÷ 8 : Remainder = 0
• Divide 168 by 12: 168 ÷ 12 : Remainder = 0
• Divide 168 by 14: 168 ÷ 14 : Remainder = 0
• Divide 168 by 21: 168 ÷ 21 : Remainder = 0
• Divide 168 by 24: 168 ÷ 24 : Remainder = 0
• Divide 168 by 28: 168 ÷ 28 : Remainder = 0
• Divide 168 by 42: 168 ÷ 42 : Remainder = 0
• Divide 168 by 56: 168 ÷ 56 : Remainder = 0
• Divide 168 by 84: 168 ÷ 84 : Remainder = 0
• Divide 168 by 168: 168 ÷ 168 : Remainder = 0

Hence, Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168

#### 2. Steps to find factors of 168 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 168 using the division method, follow these steps:

• Step 1. Start dividing 168 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 168, which is 2. Divide 168 by 2 to obtain the quotient (84).
168 ÷ 2 = 84
• Step 3. Repeat step 1 with the obtained quotient (84).
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So, the prime factorization of 168 is, 168 = 2 x 2 x 2 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 168 as shown below:

So, the prime factorization of 168 is, 168 = 2 x 2 x 2 x 3 x 7.

#### 3. Find factors of 168 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 168 would be the two numbers which, when multiplied, give 168 as the result.

The following table represents the calculation of factors of 168 in pairs:

Factor Pair Pair Factorization
1 and 168 1 x 168 = 168
2 and 84 2 x 84 = 168
3 and 56 3 x 56 = 168
4 and 42 4 x 42 = 168
6 and 28 6 x 28 = 168
7 and 24 7 x 24 = 168
8 and 21 8 x 21 = 168
12 and 14 12 x 14 = 168

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 168. They are called negative pair factors.

Hence, the negative pairs of 168 would be ( -1 , -168 ) , ( -2 , -84 ) , ( -3 , -56 ) , ( -4 , -42 ) , ( -6 , -28 ) , ( -7 , -24 ) , ( -8 , -21 ) and ( -12 , -14 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 168 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 168.
• Every number is a factor of zero (0), since 168 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, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 are exact divisors of 168.
• Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. Each factor divides 168 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 are all less than or equal to 168.

• How do you find factors of a negative number? ( eg. -168 )?

Factors of -168 are -1, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -56, -84, -168.

• What is the sum of all factors of 168?

The sum of all factors of 168 is 480.

• What is prime factorization of 168?

Prime factorization of 168 is 2 x 2 x 2 x 3 x 7.

• What are the pair factors of 168?

Pair factors of 168 are (1,168), (2,84), (3,56), (4,42), (6,28), (7,24), (8,21), (12,14).

• What are six multiples of 168?

First five multiples of 168 are 336, 504, 672, 840, 1008, 1176.

• Is 168 a whole number?

Yes 168 is a whole number.

• Which is the smallest prime factor of 168?

Smallest prime factor of 168 is 2.

• What are five multiples of 168?

First five multiples of 168 are 336, 504, 672, 840, 1008.

• Write all factors of 168?

Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.

#### Examples of Factors

Joey wants to write all the prime factors of 168 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 168 are 2, 2, 2, 3, 7.
So in exponential form it can be written as 23 x 3 x 7.

How many factors are there for 168?

Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 168. Can you predict the answer?

15 factor(s) of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84.

Sammy is puzzled while calculating the prime factors of 168. Can you help him find them?

Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
Prime factors of 168 are 2, 2, 2, 3, 7

What is prime factorization of 168?

Prime factorization of 168 is 2 x 2 x 2 x 3 x 7 = 23 x 3 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 168. Can you help her?

Prime factors of 168 are 2, 2, 2, 3, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 168?

Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
Even factors of 168 are 2, 4, 6, 8, 12, 14, 24, 28, 42, 56, 84, 168.
Hence, product of even factors of 168 is; 2 x 4 x 6 x 8 x 12 x 14 x 24 x 28 x 42 x 56 x 84 x 168 = 1438916737499136.