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Factors

What Are the Factors of 24? | Prime Factorisation and Factor Tree of 24

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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What Are the Factors of 24? | Prime Factorisation and Factor Tree of 24

What Are the Factors of 24? | Prime Factorisation and Factor Tree of 24

Factors of 24 are those numbers that are completely divisible by 24 without leaving any remainder. In other words, if two numbers are multiplied and their result comes out to be 24, those numbers are factors of 24. There are a total of 8 factors of 24, with 24 being the highest factor of the number 24. Factors of 24 pairs have a negative and a positive pair. In this article, we will discuss the factors of 24, how to find them, prime factorization, and the factor tree of 24, along with some solved examples. Scroll down to find more.

What Are the Factors of 24?

The factors of 24 can be defined as the numbers which are completely divisible by the number 24, or you can define it as two numbers when multiplied by each other, giving the result of 24. The factors of 24 can be listed as 1, 2, 3, 4, 6, 8, and 24. The factors of 24 have both a positive pair and a negative one. Negative pair factors of 24 can be obtained by multiplying two negative numbers, i.e., (-24) X (-1) = -24. The positive pair factors of 24 can be obtained by -1, -2, -3, -4, -6, -8, -12, and -24.

  • Factors of 24 = 1, 2, 3, 4, 6, 8 and 24
  • Negative Pair Factors of 24 = -1, -2, -3, -4, -6, -8, -12 and -24.

Factors of 24 in Pairs

The factors of 24 has both positive and negative pairs. The positive and negative pair factors of 24 are given below:

Positive Pair Factors of 24

The positive pair factors of 24 are given below:

Positive Pair Factors of 24

Negative Pair Factors of 24

The negative pair factors of 24 are given below:

Negative Pair Factors of 24

How to Calculate the Factors of 24?

Factors of 24 are a list of whole numbers that can divide 24 into equal parts and not leave any remainder. Hence, these numbers cannot be a fraction or decimals. The steps to find factors of 24 are given below:

Using the Multiplication Method

  • Step 1: We can calculate the factors of 24 using the multiplication method. For this method we check what pairs of numbers can be multiplied with each other in order to get the result 24. So, for this, we need to multiply the number 24 by a series of natural numbers, from 1 to 24. The numbers that get completely divided by 24, without leaving any remainder, are the factors of 24.
  • Step 2: We know that the multiples of 24 are those numbers that are completely divided by 24. Now, let’s create a list of those numbers and its pair. For example, 1 X 24=24 and
    2 X 12= 24, so (1,24) is the first pair and (2,12) is the second pair, and so on.
Factor of 24
1 X 24= 24
2 X 12= 24
3 X 8= 24
4 X 6= 24

From the above table, it is clear that factors of 24 are 1, 2, 3, 4, 5, 6, 12, and 24.

Using the Division Method

  • Step 1: A number is a factor of itself, and 1 is the factor of all natural numbers. So, 1 and 24 are factors of 24. 24 is an even number, so it is divisible by 2, so 2 is a factor of 24. 24 is also a multiple of 3, 4, 6, 8, and 12.
Factor of 24
24 ÷ 1= 24
24 ÷ 2= 12
24 ÷ 3= 8
24 ÷ 4= 6
24 ÷ 6= 4
24 ÷ 8= 3
24 ÷ 12= 2
24 ÷ 24= 1

Hence, the factors of 24 are 1, 2, 3, 4, 6, 12, and 24.

What Is the Prime Factorisation of 24?

Through prime factorization, we can find the prime factors of 24. The steps to find the prime factorisation of 24 are given below:

  • Step 1: Divide 24 by the smallest prime number. Hence, the least prime number that is divisible by 24 is 2.
  • Step 2: When 24 is divided by 2, we will get the number 12.
  • Step 3: Since 12 is a composite number, we need to divide the number with the least prime number. which is 2.
  • Step 4: Dividing 12 by 2 gives 6.Now, divide 6 by 2, which gives a result of 3.
  • Step 5: Now, if you divide 3 by 2, you will get a fraction number, so let’s divide 3 with the next prime number, i.e., 3 /3 = 1.

Hence, we have 1 as the end result, so we cannot proceed any further. So, the prime factorization of 24 is 2 X 2 X 2 X 3 = 24, where 2 and 3 are prime numbers and the prime factors are 2 and 3.

Prime Factorization of 24

What Is the Factor Tree of 24?

We can also find the prime factors of the number 24 using the factor tree method. The steps to find prime factors of number 24 using the factor tree method are given below:

  • Step 1: Place the number 24 at the top of the factor tree.
  • Step 2: Now, as the tree branches, we will write down the pair factors of 24. Here we are using the pair factor 2, 12 as the first branch of 24.
  • Step 3: 2 and 12 are factor pairs of 24. Now, let’s divide 12 further as it is a composite number.
  • Step 4: Let’s repeat the processes of factorization and splitting until we reach a prime number.
  • Step 5: So, in the next tree branch we get 6, 2, and 6. Then, let’s split 6 further, as 6 is a composite number.
  • Step 6: When we split 6, we get 3, and 2 is the next tree branch. Now, both 3 and 2 are prime numbers, so this is the end factor pair.

Since all the factors of all the numbers are prime numbers, we can’t split the numbers 2 and 3 anymore as they are prime numbers.

The factor tree of 24 is given below:

Factor tree of 24

What Are the Factors of 24 Listed From Least to Greatest?

The factors of 24 are 2, 3, 6,4,12, 1, and 24
Now, let’s arrange the factors of 24 from least to greatest or in increasing order.
Hence, the factors of 24 in increasing order is 1, 2, 3, 4, 6, 12, and 24.

Solved Examples of Factor of 24

Q 1: Write all positive factors of 24.
A 1:
All positive factors of 24 are 1, 2, 3, 4, 6, 12, and 24.

Q 2: What are the positive and negative pair factors of 24?
A 2:
The positive pair of factors of 24 are (1, 24), (2, 12), (3, 8), and (4, 6). The negative pair of factors of 24 are (-1, -24), (-2, -12), (-3, -8), and (-4, -6).

Q 3: Find out the highest common factor of 24 and 6.
A 3:
The factors of 24 are 1, 2, 3, 4, 5, 6, 12, and 24.
The factors of 6 are 1, 2, 3, 6.
Hence, the common factors are 1, 2, 3, and 6.
Therefore, the highest common factor of 24 and 6 is 6.

Q 4: What are the factors and prime factors of 24?
A 4:
The factors of 24 are 1, 2, 3, 4, 5, 6, 12, and 24.
The prime factors of 24 are 2 and 3.

Q 5: Find the highest common factor of 24 and 8.
A 5:
The factors of 24 are 1, 2, 3, 4, 6, 12, and 24.
The factors of 8 are 1, 2, 4, and 8.
The common factors are 1, 2, and 4. So, the highest common factor is 4.

FAQs on Factors of 24

What are the factors of 24 in pairs?
The factors of 24 in pairs are (1, 24), (2, 12), (3, 8), and (4, 6).

What is the sum of the factors of 24?
The factors of 24 are 1, 2, 3, 4, 6, 12, and 24.
Now, let’s add all the factors 1+2+3+4+6+8+12+24=60.
Therefore, the sum of all the factors of 24 is 60.

Find all the factors of 24.
All the factors of 24 are 1, 2, 3, 4, 5, 6, 12, and 24.

Find the common factors between 24 and 36.
The factors of 24 are 1, 2, 3, 4, 6, 12, and 24.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Therefore, the common factors are 1, 2, 3, 4, 6, and 12.

What are the common factors of 24 and 18?
The factors of 24 are 1, 2, 3, 4, 6, 12, and 24.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
Therefore, the common factors are 1, 2, 3, and 6.

What are the common factors between 24 and 32?
Factors of 24: 1, 2, 3, 4, 6, 12, and 24.
Factors of 32: 1, 2, 4, 8, 16, 32, and 64.
Hence, the common factors of 24 and 32 are 1, 2, and 4.
Also, the least common factor of 24 and 32 is 1 and the greatest common factor of 24 and 32 is 4.

What are the common factors between 24 and 60?
Factors of 24: 1, 2, 3, 4, 6, 12, and 24.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Hence, the common factors of 24 and 60 are 1, 2, 3, 4, 6, and 12.
Also, the least common factor of 24 and 60 is 1 and the greatest common factor of 24 and 60 is 12.

We hope this article on factors of 24 is helpful to you. If you have any questions related to this page, ping us through the comment section below and we will get back to you as soon as possible.

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Prerit Jain

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