What are the factors of 24?
The factors of 24 are those integers that divide 24 without leaving any remainder, or we can say that the factors of 24 will divide it evenly.
The factors of 24 can be positive as well as negative, but they cannot be a decimal or a fraction. The quotient obtained on dividing 24 by its factor is also a factor of 24.
For example, 3 is a factor of 24 because when we divide 24 by 3, it leaves the remainder equal to 0, and 8, which appears as a quotient in this division, is also a factor of 24.
Factor list for the number 24
The factors of 24 can be obtained by applying divisibility rules and division facts.
The Prime Factors of 24
A factor tree can be used to determine the prime factors of 24, as shown in the figure.
From the factor tree, we can see that the prime factorization of 24 is 2 × 2 × 2 × 3.
This means 2 and 3 are the only prime factors of 24.
Factor Pairs of 24
The factor pair of any number is a set of two integers that, when multiplied, result in that number. So, the two integers are factors of the number. A factor pair can be negative or positive.
[Note: The product of two negative numbers is positive.]
The factor pair of 24 is the set of two factors of 24 that, when multiplied, give 24 as the
product.
Thus, the factor pairs of 24 can be obtained from the list of its factors.
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Rapid Recall
Solved Factors of 24 Examples
Example 1: Find the common factors of 10 and 24.
Solution:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 10: 1, 2, 5, 10,
So, the common factors of 10 and 24 are 1 and 2.
Hence, 10 and 24 have two common factors, 1 and 2.
Example 2: John wants to organize 24 pictures into a rectangular array on a wall. How many different arrays can he make?
Solution:
To find the number of ways John can organize 24 pictures into a rectangular array, we need to find the number of different sets of length and width of the rectangular array whose area will be 24 units.
The product of the factor pair of 24 = the area of a rectangular array (24 units)
The area of a rectangular array = length x width
So, the product of the factor pair of 24 = length x width
There are four factor pairs of 24. Each pair can make two rectangular arrays.
For example, the factor pair 24, 1 can make one rectangular array with a length of 24 units and a width of 1 unit and a second rectangular array with a length of 1 unit and a width of 24 units.
Hence, the different rectangular arrays in which John can organize the pictures are-
1 x 24, 2 x 12, 3 x 8, 4 x 6, 24 x 1, 12 x 2, 8 x 3 , and 6 x 4.
Hence, there are eight ways to organize the 24 pictures in rectangular arrays.
Example 3: What are the common factors of 24 and 18?
Solution:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
Hence, the common factors of 24 and 18 are 1, 2, 3, 9, and 18.
The number 11 does not divide 24 exactly. It leaves a remainder greater than zero. So, 11 is not a factor of 24.
Yes, 24 is a composite number as it has factors other than 1 and itself, that is, 24. In other words, the number 24 has more than two factors. It has the factors 2, 3, 4, 6, 8, and 12 other than 1 and 24.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
So, the least factor of 24 is 1, and the greatest factor is 24 itself.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Hence, the sum of all the factors of 24 is
= 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60
Hence, the sum is 60.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
So, the number 24 has eight factors.