Factors of 168
Factors of 168 are the numbers that can divide 168 evenly. 168 is a threedigit even number, and certainly, it has many factors, most of which are even. There are 16 factors of 168 in all. Of course, since the three digits add up to a multiple of 3, 168 is also divisible by 3. In this lesson, we will calculate the factors of 168, its prime factors, and its factors along with some solved examples for better understanding.
 Factors of 168 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
 Negative Factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
 Prime Factorization of 168: 168 = 2^{3} × 3 × 7
What are Factors of 168?
Factors of 168 are the numbers that divide it completely and give the remainder as 0. When you multiply any two natural numbers with each other and get 168 as the answer, you can say that both numbers will be the factors of 168.
For example, you can get 168 as an answer with the following numbers:
 1 × 168 = 168
 2 × 84 = 168
 3 × 56 = 168
 4 × 42 = 168
 6 × 28 = 168
 7 × 24 = 168
 8 × 21 = 168
 2 × 14 = 168
This can be continued until you reach 168 × 1 = 168. Thus, in general, we can say that the factors of 168 are all the integers that divide 168 without leaving any remainder.
How to Calculate the Factors of 168?
Let's begin calculating the factors of 168, starting with the smallest natural number, i.e. 1. Divide 168 with this number. Is the remainder 0? Yes! So, we will get:
 168 ÷ 1 = 168
 168 × 1 = 168
The next natural number is 2. Now, divide 168 with 2.
 168 ÷ 2 = 84
 84 × 2 = 168
Proceeding in a similar manner, we get:
 1 × 168 = 168
 2 × 84 = 168
 3 × 56 = 168
 4 × 42 = 168
 6 × 28 = 168
 7 × 24 = 168
 8 × 21 = 168
 12 × 14 = 168
Factors of 168 By Prime Factorization
Prime factorization means to express a composite number as the product of its prime factors.
Prime Factorization by Division
 Step 1: To get the prime factorization of 168, we divide it by its smallest prime factor which is 2 i.e. 168 ÷ 2 = 84
 Step 2: Now, 84 is divided by its smallest prime factor and the quotient is obtained.
 Step 3: This process is repeated till we get the quotient as 1.
Prime Factorization by Factor Tree
We can do the same procedure using the factor tree as shown in the diagram given below:
Prime Factorization by UpsideDown Division
The prime factorization of 168 is shown below:
Let us express 168 in terms of the product of its prime factors as 2 × 2 × 2 × 3 × 7.
Q: Now that we have done the prime factorization of our number, we can multiply the numbers and get the other factors. Can you try and find out if all the factors are covered or not?
A: As you may have already guessed, for prime numbers, there are no other factors. Explore factors using illustrations and interactive examples:
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
 Factors of 15  The factors of 15 are 1, 3, 5, and 15.
 Factors of 45  The factors of 45 are 1, 3, 5, 9, 15, and 45.
 Factors of 72  The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.
 Factors of 48  The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Challenging Questions:
 Determine a few other numbers that have only a onefactor pair.
 Can multiples of 168 also be factors of 168?
Factors of 168 in Pairs
The pairs of numbers which give 168 when multiplied are known as the factor pairs of 168. The following are the factors of 168 in pairs:
Product form of 168 
Pair factor 
1 × 168 = 168 
(1,168) 
2 × 84 = 168 
(2, 84) 
3 × 56 = 168 
(3, 56) 
4 × 42 = 168 
(4, 42) 
6 × 28 = 168 
(6, 28) 
7 × 24 = 168 
(7, 24) 
8 × 21 = 168 
(8, 21) 
12 × 14 = 168 
(12, 14) 
14 × 12 = 168 
(14,12) 
21 × 8 = 168 
(21, 8) 
You can observe in the table above, after 12 × 14, the factors start repeating, except that they appear in a different order. So, it is enough to find factors until (12, 14)
Pairs of factors of 168 are: (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21) and (12, 14).
Let's take a look at the negative pair factors of 168.
 If we consider negative integers, both the numbers in the pair factors will be negative.
 It is possible to have negative pair factors as well because the product of two negative numbers gives a positive number.
 Thus, we can have factor pairs of 168 as (1,168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21) and (12, 14).
Important Notes:
 The smallest factor of 168 is 1 and the largest factor of 168 will be the number itself, i.e. 168.
 Fractions and decimals cannot be factors. Only integers (positive or negative) can be factors.
 Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
Factors of 168 Solved Examples

Example 1: Find the factor of 168 which is also half of 168.
Solution:
Half of 168 = 1/2 × 168 = 84. Thus, 84 is the factor of 168 which is also half of 168.

Example 2: Help John determine the number which on multiplying with 168 gives 168.
Solution:
The negative factor pair of 168 is (1,168). When 168 is multiplied by 1, the product is 168 i.e. 168 × 1 =168
Thus, 1 is the number which on multiplying with 168 gives 168.
FAQs on Factors of 168
What are the Prime Factors of 168?
The prime factors of 168 are 2, 3, and 7.
What are the Positive Pair Factors of 168?
The factors of 168 in pairs are (1,168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21) and (12, 14).
What are the Negative Pair Factors of 168?
The negative factors of 168 in pairs are (1,168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21) and (12, 14).
How many Factors of 168 are there?
Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168. Thus, there are 16 factors.
What are the Factors of 168?
Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
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