Factors of 168

The numbers that divide 168 evenly are known as factors of 168. A factor of 168 is a number that divides the number without remainder. The factors of 168 are 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 factors of 168: 2, 3, and 7.

Prime factorization of 168: 2³ × 3 × 7.

The sum of factors of 168: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 21 + 24 + 28 + 42 + 56 + 84 + 168 = 360

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 168. Identifying the numbers which are multiplied to get the number 168 is the multiplication method.

Step 1: Multiply 168 by 1, 168 × 1 = 168.

Step 2: Check for other numbers that give 168 after multiplying

2 × 84 = 168

3 × 56 = 168

4 × 42 = 168

6 × 28 = 168

7 × 24 = 168

8 × 21 = 168

12 × 14 = 168

Therefore, the positive factor pairs of 168 are: (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14). All these factor pairs result in 168. For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 168 by 1, 168 ÷ 1 = 168.

Step 2: Continue dividing 168 by the numbers until the remainder becomes 0.

168 ÷ 1 = 168

168 ÷ 2 = 84

168 ÷ 3 = 56

168 ÷ 4 = 42

168 ÷ 6 = 28

168 ÷ 7 = 24

168 ÷ 8 = 21

168 ÷ 12 = 14

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

The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 168 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

168 ÷ 2 = 84

84 ÷ 2 = 42

42 ÷ 2 = 21

21 ÷ 3 = 7

7 ÷ 7 = 1

The prime factors of 168 are 2, 3, and 7. The prime factorization of 168 is: 2³ × 3 × 7.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 168 is divided by 2 to get 84.

Step 2: Now divide 84 by 2 to get 42.

Step 3: Then divide 42 by 2 to get 21.

Step 4: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 168 is: 2³ × 3 × 7.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 168: (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14).
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• Negative factor pairs of 168: (-1, -168), (-2, -84), (-3, -56), (-4, -42), (-6, -28), (-7, -24), (-8, -21), (-12, -14).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 168.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 168 are (1, 168), (2, 84), etc.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 168 is 2³ × 3 × 7.

• Multiple: A multiple is a number that can be divided by another number without a remainder. For example, 168 is a multiple of 4.