What are the Factors of 168?
The factors of 168 are those integers that divide 168 without leaving any remainder. The factors of 168 cannot be decimals or fractions.
Factors of 168:
Factors | Pair factors | Prime factorization |
|---|---|---|
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 | (1, 168), (2, 84), (3, 56) (4, 42), (6, 28), (7, 24), (8, 21), (12, 14) | 168 = 2 x 2 x 2 x 3 x 7 |
Factor list for 168
Factors | Pair factors | Prime factorization |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 168 = 168 |
2 | Yes, 168 is even. | 2 × 84 = 168 |
3 | Yes, 1 + 6 + 8 = 15, 15 is divisible by 3 | 3 × 56 = 168 |
4 | Yes, 168 ÷ 4 = 42R0 | 4 × 42 = 168 |
5 | No, the ‘ones’ digit is not 0 or 5. | - |
6 | Yes, 168 is even and divisible by 3. | 6 × 28 = 168 |
7 | Yes, 168 ÷ 7 = 24R0 | 7 x 24 = 168 |
8 | Yes, 168 ÷ 8 = 21R0 | 8 × 21 = 168 |
9 | No, 1 + 6 + 8 = 15, 15 is not divisible by 9 | - |
10 | No, the ‘ones’ digit is not 0. | - |
11 | No, 168 ÷ 11 = 15R3 | - |
12 | Yes, 168 ÷ 12 = 14R0 | 12 × 14 = 168 |
13 | No, 168 ÷ 13 = 12R12 | - |
14 | Yes, 168 ÷ 14 = 12R0 | 14 × 12 = 168 |
We stop checking now as the factor pairs start repeating.
Explaining the prime factors of 168
Below is the factor tree of 168:
From the factor tree, we can see that the prime factorization of 168 is: 2 x 2 x 2 × 3 × 7 = 2\(^3\) x 3 x 7
Therefore, 2, 3, and 7 are the prime factors of 168.
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The factor pairs of 168
A factor pair of 168 is a pair of factors of 168 which when multiplied together, results in 168.
The factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
Positive factors of 168 | Positive pair factors of 168 |
|---|---|
1 x 168 | (1, 168) |
2 x 84 | (2, 84) |
3 x 56 | (3, 56) |
4 x 42 | (4, 42) |
6 x 28 | (6, 28) |
7 x 24 | (7, 24) |
8 x 21 | (8, 21) |
12 x 14 | (12, 14) |
Rapid recall
Solved Factors of 168 Examples
Example 1: Find the common factors of 20 and 168.
Solution:
Factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168
Factors of 20: 1, 2, 4, 5, 10, and 20.
So, the common factors of 20 and 168 are 1, 2, and 4.
Hence, 20 and 168 have 3 common factors.
Example 2: How many factors does 168 have?
Solution:
The factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
So, there are 16 factors of the number 168.
Example 3: How many factor pairs does 168 have?
Solution:
A set of two factors of 168, which when multiplied together results in 168, is known as the factor pairs of 168.
The factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
Factor pairs of 168 are (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21) and (12, 14).
Hence, 168 has a total of eight factor pairs.
Yes, 8 is a factor of 168. The number 8 divides 168 exactly, that is, it leaves 0 as the remainder. So, 8 is a factor of 168.
Yes, 168 is a composite number as it has factors other than 1 and itself. It has factors of 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, other than 1 and 168.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
So, the least factor of 168 is 1, and the greatest factor is 168 itself.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
Hence, the sum of the all the factors of 168 is
= 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 21 + 24 + 28 + 42 + 56 + 84 + 168 = 480
Hence, the sum is 480.