What Is The Prime Factor Of 24:
The prime factor of 24 is 2, 3, and 6. This means that the characteristics of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The number 1 is not a prime number, so it does not have any prime factors. 2 is the only prime number that appears twice in the list of factors for 24. 3 and 6 are the superior prime numbers that occur once in the list for 24.
The other numbers in the list are composites, meaning they are created by multiplying two or smaller numbers together. For example, 4 = 2 x 2, 12 = 2 x 3 x 4, and 24 = 2 x 3 x 2 x 3. Composites can be further decomposed into their prime factors, but 2, 3, and 6 cannot be further divided. This makes them called the “prime factors” of 24.
One way to think about the prime factors of a number is to imagine breaking the number down into smaller and smaller pieces. For example, if someone asked you to divide 24 into smaller chunks, you might start by dividing it by two since 2 is a prime number, and it’s one of the factors of 24. You would end up with 12 ÷ 2 = 6.
Then you could divide six by two again to get 3, and so on. If you continue this process long enough, you will eventually reach 1, the smallest possible number divided. This is why 1 is not a prime number – it can’t be divided any further.
A factor tree can also determine the prime factors of a number. A factor tree is a diagram that helps visualize the prime factors of a number. It starts with the number at the top of the tree and then splits it into smaller and smaller pieces until you reach 1, represented by a branch that goes off to the side. The prime factors are located at the ends of each unit. Here’s an example factor tree for 24:
As you can see, the prime factors of 24 are 2, 3, and 6. This information can be helpful when trying to figure out how to best split up a number into smaller chunks. For example, if you were trying to divide 24 students into groups of four, you could use the prime factors of 24 to help you determine how many groups of four students you could create.
Since 2 x 3 = 6, you could create two groups of four students and one group of three students. You could also create three groups of four students or four groups of three students, but you couldn’t make a group of five or six students because those numbers are not factors of 24.
The prime factors of a number can also be used to find the most significant common factor (GCF) and the least common multiple (LCM) of two numbers. The GCF is the most important number that is a factor of both numbers. The LCM is the smallest number that is a multiple of both numbers.
Here’s an example:
The GCF of 24 and 30 is 6, and the LCM of 24 and 30 is 120.
The prime factors of 30 are 2, 3, 5, and 10. The prime factors of 24 are 2, 3, and 6. Since 2 x 3 = 6 is the GCF of 24 and 30, the prime factors of both numbers are the same. This makes sense because 24 and 30 are both divisible by 6.
The LCM of 24 and 30 is also 120, which happens to be the product of the prime factors of both numbers (2 x 3 x 5 x 10 = 120).
The prime factors of a number can also be used when looking for patterns in the multiplication table.
For example, let’s look at the multiplication table for 18:
We can see that each column and every row contain the same prime number (2), but we’re most interested in what happens in the highlighted section. The two numbers in this section are 3 and 6, and they both appear in all of the rows and columns that intersect. This makes sense because 18 is divisible by both 3 and 6.
If you reduce 18 to its prime factors, you will find 2 x 2 x 3 x 3 = 36. This means that the product of multiplying any two numbers together within this section will always result in 36.
You can use the same process to look for any number of patterns within the multiplication table. For example, if you wanted to find the prime factors of 25, you could use it to find five different ways in the table below. Each print has its color so that it’s easier to follow:
Each of these patterns can be found by reducing each factor until they only have one digit left. The characteristics of 5 are 5 and 1, which reduces down to 2 x 2. You can then reduce this further into 1 x 2 = 2. The factors of 7 are 7 and 1, which reduces down to 6 x 1. Then you reduce this again into 6 x 6 = 36.
The GCF within this section is 1, and the LCM of these numbers is 126. You can see this pattern in the multiplication table below:
This section has a GCF of 1 because all other patterns intersect to form a rectangle pattern. All of the factors within this rectangle add up to 12 + 18 + 20 = 50, which reduces down to 5 x 10 = 50. The LCM for this rectangle is also 126 since it’s formed by multiplying 7 x 8 x 9 x 10 = 630.
The GCF and LCM are helpful when looking for patterns within a multiplication table or when checking dimensional problems where you have to find how many times one number goes into another number.
For example, if you had to find how many groups of 24 students you could create using the prime factors of both numbers, you would treat it like a dimensional problem. This means that you can use division to solve how many times one number goes into another.