Factors of 24 are the list of integers that can be evenly divided into 24. There are overall 8 factors of 24 among which 24 is the biggest factor and 1, 2, 3, 4, 6, 8, 12, and 24 are positive factors. The sum of all factors of 24 is 60 and its factors in Pairs are (1, 24), (2, 12), (3, 8), and (4, 6).

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Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24Negative Factors of 24: -1, -2, -3, -4, -6, -8, -12 and -24Prime Factors of 24: 2, 3Prime Factorization of 24: 2 × 2 × 2 × 3 = 23 × 3Sum of Factors of 24: 60
1.What are Factors of 24?
2.Important Notes
3.How to Calculate Factors of 24?
4.Factors of 24 by Prime Factorization
5.Factors of 24 in Pairs
6.FAQs on Factors of 24
7.Tips and Tricks

Before we move ahead, let"s recall a little about factors. A factor is a number that divides the given number without any remainder. Factors of 24 are pairs of those numbers whose product results in 24.

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To calculate the factors of any number, here in this case 24, we need to find all the numbers that would divide 24 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 24 respectively. The number 1 and the number itself would always be a factor of the given number.

Let us check the division of 24 by its factors. We express 24 as a product of its prime factors in the prime factorization method and we divide 24 with its divisors in the division method. Let us see which numbers divide 24 exactly without a remainder in which case the divisors, as well as the quotients, are the factors of 24.

24/1 = 24; therefore, 1 and 24 are factors of 2424/2 = 12; therefore, 2 is a factor of 2424/3 = 8; therefore, 3 is a factor of 2424/4 = 6; therefore, 4 is a factor of 24

Hence, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. To understand the concept of finding factors by prime factorization better, let us take a few more examples.


Prime factorization means expressing a composite number as the product of its prime factors. Factors of 24 by prime factorization are given by using the following steps:

Step 1: Write the pair of factors, which on multiplication, gives the required number.

24 can be factored as a product of 4 and 6.

Step 2: Check each of the factors to see whether each one of them is prime or not.

4 is not a prime number and can be dissociated as a product of 2 by itself or as a square of 2.6 is not a prime number and can be dissociated as a product of 2 and 3.

Step 3: As per the criteria,

24 can be written as 24 = 4 × 6 = 2 × 2 × 2 × 3It can also be written as 24 = 23 × 3

Pair factors are pairs of those numbers that, when multiplied, give the product as the required number. Here, the required number is 24. Let"s try visualizing it using blocks.

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Factors of 24 in pairs can be written as:

FactorsPair factors
1 × 24 = 241, 24
2 × 12 = 242, 12
3 × 8 = 243, 8
4 × 6 = 244, 6
6 × 4 = 246, 4
8 × 3 = 248, 3
12 × 2 = 2412, 2
24 × 1 = 2424, 1

These factors given above are positive pair factors. It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.

Let"s have a look at negative pair factors.

FactorsPair factors
-1 × -24 = 24-1, - 24
-2 × -12 = 24-2, - 12
-3 × -8 = 24-3, -8
-4 × -6 = 24- 4, - 6
-6 × -4 = 24-6, -4
-8 × -3 = 24-8, - 3
-12 × -2 = 24- 12, -2
-24 × -1 = 24-24, -1

1 is the smallest factor of every number.Every number has a minimum of two factors, i.e. 1 and the number itself.All even numbers always have 2 as one of their factors.All the numbers which end in 5, will always have 5 as one of their factors.All the numbers which end in 0, will always have 1, 2, 5, and 10 as their factors.

Example 1: Henry has to determine which pair factor of 24 on addition gives 14, subtraction gives 10, and division gives one of the factors of 24 which belongs to another pair. Which pair factor do you think it is?

Solution:

Henry writes down the details given to him:

Addition of pair factors = 14Subtraction of pair factors = 10

Division of pair factors = One factor belonging to another pair. The pair factor is (12, 2). This pair factor on addition gives 14, on subtraction gives 10, and on division gives 6, which is another factor of 24 and is a part of another pair factor.

Therefore, (12, 2) is the required pair factor.


Example 2: Jenny has an apple tree. She plucks 24 apples from the tree every day. She has to distribute it among her 4 friends. How many apples will each friend get?

Solution:

Jenny has to divide 24 apples among her 4 friends. This means each friend gets 24/4, which is 6 apples.

Therefore, each friend will get 6 apples every day.


Example 3: How many factors are there for 24?

Solution:

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Therefore, 24 has 8 factors.


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FAQs on Factors of 24

What are the Factors of 24?

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and its negative factors are -1, -2, -3, -4, -6, -8, -12, -24.

What are the Prime Factors of 24?

The prime factors of 24 are 2, 3.

What is the Greatest Common Factor of 24 and 23?

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and the factors of 23 are 1, 23. 24 and 23 have only one common factor which is 1. This implies that 24 and 23 are co-prime.Hence, the Greatest Common Factor (GCF) of 24 and 23 is 1.

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What are the Common Factors of 24 and 21?

Since, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and the factors of 21 are 1, 3, 7, 21.Hence, <1, 3> are the common factors of 24 and 21.

What is the Sum of the Factors of 24?

Sum of all factors of 24 = (23 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) = 60