# Factors of 24

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24

#### How to find factors of a number

 1.   Find factors of 24 using Division Method 2.   Find factors of 24 using Prime Factorization 3.   Find factors of 24 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 24

• Divide 24 by 1: 24 ÷ 1 : Remainder = 0
• Divide 24 by 2: 24 ÷ 2 : Remainder = 0
• Divide 24 by 3: 24 ÷ 3 : Remainder = 0
• Divide 24 by 4: 24 ÷ 4 : Remainder = 0
• Divide 24 by 6: 24 ÷ 6 : Remainder = 0
• Divide 24 by 8: 24 ÷ 8 : Remainder = 0
• Divide 24 by 12: 24 ÷ 12 : Remainder = 0
• Divide 24 by 24: 24 ÷ 24 : Remainder = 0

Hence, Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24

#### 2. Steps to find factors of 24 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 24 using the division method, follow these steps:

• Step 1. Start dividing 24 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 24, which is 2. Divide 24 by 2 to obtain the quotient (12).
24 ÷ 2 = 12
• Step 3. Repeat step 1 with the obtained quotient (12).
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1

So, the prime factorization of 24 is, 24 = 2 x 2 x 2 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 24 as shown below:

So, the prime factorization of 24 is, 24 = 2 x 2 x 2 x 3.

#### 3. Find factors of 24 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 24 would be the two numbers which, when multiplied, give 24 as the result.

The following table represents the calculation of factors of 24 in pairs:

Factor Pair Pair Factorization
1 and 24 1 x 24 = 24
2 and 12 2 x 12 = 24
3 and 8 3 x 8 = 24
4 and 6 4 x 6 = 24

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 24. They are called negative pair factors.

Hence, the negative pairs of 24 would be ( -1 , -24 ) , ( -2 , -12 ) , ( -3 , -8 ) and ( -4 , -6 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

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

• How do you find factors of a negative number? ( eg. -24 )?

Factors of -24 are -1, -2, -3, -4, -6, -8, -12, -24.

• What is the sum of all factors of 24?

The sum of all factors of 24 is 60.

• What is prime factorization of 24?

Prime factorization of 24 is 2 x 2 x 2 x 3.

• What are the pair factors of 24?

Pair factors of 24 are (1,24), (2,12), (3,8), (4,6).

• What are six multiples of 24?

First five multiples of 24 are 48, 72, 96, 120, 144, 168.

• Is 24 a whole number?

Yes 24 is a whole number.

• Which is the smallest prime factor of 24?

Smallest prime factor of 24 is 2.

• What are five multiples of 24?

First five multiples of 24 are 48, 72, 96, 120, 144.

• Write all factors of 24?

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

#### Examples of Factors

Joey wants to write all the prime factors of 24 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 24 are 2, 2, 2, 3.
So in exponential form it can be written as 23 x 3.

How many factors are there for 24?

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 24. Can you predict the answer?

7 factor(s) of 24 are 1, 2, 3, 4, 6, 8, 12.

Sammy is puzzled while calculating the prime factors of 24. Can you help him find them?

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Prime factors of 24 are 2, 2, 2, 3

What is prime factorization of 24?

Prime factorization of 24 is 2 x 2 x 2 x 3 = 23 x 3.

Ariel has been assigned the task to find the product of all the prime factors of 24. Can you help her?

Prime factors of 24 are 2, 2, 2, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 24?

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Even factors of 24 are 2, 4, 6, 8, 12, 24.
Hence, product of even factors of 24 is; 2 x 4 x 6 x 8 x 12 x 24 = 110592.