# Factors of 168

Factors of 168 are the natural numbers, by which the original number is completely divisible. When the product of two whole numbers is equal to 168, then these numbers are referred to as factors. Since the factors divide the original number, therefore they are also called the divisors of 168. Also, 168 is an even composite number, thus it will have more than two factors. The factors of 168 can be positive or negative, but they cannot be decimal or fraction. For example, the pair of 168 is expressed as (1, 168) or (-1, -168).

In this article, we are going to discuss what are the factors of 168, the positive and negative pair factors of 168 and the prime factorization of 168 with many examples.

## What are the Factors of 168?

The numbers that divide the number 168 exactly without leaving any remainder are the factors of 168. As the number 168 is a composite number, it has many factors other than 1 and 168. Thus, the factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168. Similarly, the negative factors fo 168 are 1-, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -56, -84, and -168.

 Factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168. Prime Factorisation of 168: 2 × 2 × 2 × 3× 7 or 23×3×7.

## Pair Factors of 168

When the product of two integers is equal to 168, then two such integers are the pair factors of the original number. Hence,

• 1 × 168 = 168
• 2 × 84 = 168
• 3 × 56 = 168
• 4 × 42 = 168
• 6 × 28 = 168
• 7 × 24 = 168
• 8 × 21 = 168
• 12 × 14 = 168

Therefore, the positive pair factors of 168 are (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14), (14, 12) and (21, 8).

We can also consider multiplying the same pair factors with negative signs, to get the positive original number.

• -1 × -168 = 168
• -2 × -84 = 168
• -3 × -56 = 168
• -4 × -42 = 168
• -6 × -28 = 168
• -7 × -24 = 168
• -8 × -21 = 168
• -12 × -14 = 168

Therefore, the negative pair factors are (-1, -168), (-2, -84), (-3, -56), (-4, -42), (-6, -28), (-7, -24), (-8, -21), (-12, -14), (-14, -12) and (-21, -8).

## How to Find the Factors of 168?

Factors of 168 can be determined by dividing the original number by the other natural numbers. If there is no remainder left after division, then the divisor is the factor.

• 168 ÷ 1 = 168
• 168 ÷ 2 = 84
• 168 ÷ 3 = 56
• 168 ÷ 4 = 42
• 168 ÷ 6 = 28
• 168 ÷ 7 = 24
• 168 ÷ 8 = 21
• 168 ÷ 12 = 14
• 168 ÷ 14 = 12
• 168 ÷ 21 = 8
• 168 ÷ 24 = 7
• 168 ÷ 28 = 6
• 168 ÷ 42 = 4
• 168 ÷ 56 = 3
• 168 ÷ 84 = 2
• 168 ÷ 168 = 1

Therefore, there are a total sixteen factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.

## Prime Factorisation of 168

Prime factorisation of 168 will result in the prime factors of the original number. In this method, we need to divide the number by prime numbers only, in increasing order of primes. Suppose 168 is divisible by the smallest prime number, i.e., 2, then 2 is the prime factor of 168. Again, the quotient is divided by the same prime number or the next prime number, by which the number is divisible. Let us see how it works.

 Dividing 168 by the smallest prime number 168 ÷ 2 = 84 84 is again divisible by 2 84 ÷ 2 = 42 42 is an even number and divisible by 2 42 ÷ 2 = 21 Now, 21 is divisible by the next prime number, i.e.3 21 ÷ 3 = 7 7 is a prime number itself 7 ÷ 7 = 1

Therefore, the prime factors of 168 are 2, 3 and 7.

Hence, the prime factorisation of 168 is 2 × 2 × 2 × 3 × 7 or 23 × 31 × 71.

## Solved Examples

Q.1: Which number should be multiplied to 21 to get 168?

Solution: Suppose, n is the number to be multiplied by 21 to get 168.

So, n × 21 = 168

n = 168/21

n = 8

Therefore, 8 should be multiplied by 21 to get 168 as the answer.

Q.2: What is the greatest common factor of 160 and 168?

Solution: The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

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

Therefore, the greatest common factor of 160 and 168 is:

GCF (160, 168) = 8

Q.3: What is the HCF of 168 and 240?

Solution: Finding the factors of both the numbers.

168 → 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

240 → 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

Therefore, HCF of 168 and 240 is 24.

### Practice Questions

1. What are the factors of 168, that are divisible by 2?
2. Find the common factors of 168 and 165.
3. Is 21 a factor of 168?
4. What should be multiplied by 24 to get 168?

## Frequently Asked Questions on Factors of 168

### What are the factors of 168?

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

### What are the multiples of 168?

The first ten multiples of 168 are 168, 336, 504, 672, 840, 1008, 1176, 1344, 1512 and 1680.

### What is the prime factor form of 168?

The prime factor form of 168 is 2 x 2 x 2 x 3 x 7.

### Is 168 a perfect square?

168 is not a perfect square. No natural number can be squared to get 168.

### Is 168 composite or prime?

168 is a composite number. It has more than two factors.