Factors of 48 – Definition and Prime Factorization
Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get any given number. Let’s take an example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6. In this session we will study the factors of 36 definitions, how to find the factors of 36 and examples. Let’s discuss the factors of 48.
What are Factors?
Factors can be defined as the numbers you multiply to get another number. There are many numbers that have more than one factorization (it means that they can be factored in more than one way). For instance, the number 12 can be factored as 1×12 or 2×6 or 3×4. Here’s what a prime factor is!A number that can only be factored as 1 times it is known as a prime number.Factors of 48 DefinitionThe factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors of any number can be either positive or negative integers.Factors of 48 are all the integers that can evenly divide the given number 48.Now let us find all factors of 48.
How to Find the Factors of 48(Prime Factorization of 48)?
According to the definition of factors of 48 we know that all factors of 48 are all the positive or negative integers which divide the number 48 completely. So let us simply divide the number 48 by every number which completely divides 48 in ascending order till 48.
48 ÷ 1 = 48
48 ÷ 2 = 24
48 ÷ 3 = 16
48 ÷ 4 = 12
48 ÷ 6 = 8
48 ÷ 8 = 6
48 ÷ 12= 4
48 ÷ 16 = 3
48 ÷ 24 = 2
48 ÷ 48 = 1
So the factors of 48-1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
We know that factors also include negative integers hence we can also have, list of negative factors of 48 are -1,-2,-3,-4,-6,-8,-12,-16,-24 and -48.
What are the Factors of 48 (Prime Factorization of 48)?1 x 48 = 48, 2 x 24 = 48, 3 x 16 = 48, 4 x 12 = 48, 6 x 8 = 48 Factors of 48 can be Listed as Follows. Positive
Factors of 48
1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
Negative Factors of 48-1,-2,-3,-4,-6,-8,-12,-16,-24 and -48
Hence 48 have a total 10 positive factors and 10 negative factors.
Pair Factors of 48 (Prime Factorization of 48)
Let’s know the pair factors of 48.
Factor Pairs of 48 are combinations of two factors that when multiplied together give 48.
List of all the Positive Factor Pairs of 48
1 x 48 = 48
2 x 24 = 48
3 x16 = 48
4 x 12 = 48
6 x 8 = 48
8 x 6 = 48
12x 4 = 48
16 x 3 = 48
24 x 2 = 48
48 x 1 = 48
As we know that all Factors of 48 include negative integers too. List of all the Negative Factor Pairs of 48:
-1 x -48 = 48
-2 x -24 = 48
-3 x-16 = 48
-4 x -12 = 48
-6 x- 8 = 48
-8 x- 6 = 48
-12x- 4 = 48
-16 x- 3 = 48
-24 x- 2 = 48
-48 x -1 = 48
Factors Of 48
To determine the factor of 48, we first have to check whether it is a prime number or a composite number. The number 48 comes out to be a composite number as it has more than two factors ( 1 and 48 itself). Therefore, we have to now find all its factors which come out to be 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. If you check, you will see that the number 48 is divisible by all these numbers.
Examples for Finding Factors of Other Numbers
Example: Find the factors of 20
Solution: The number 20 is divisible by 1, 2, 4, 5, 10 and 20. So, these six numbers are its factors
Example: Find the factors of 36
Solution: We can see that the number 36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18 and 36. Therefore, all these numbers are factors of 36.
What is Prime Factorization?
When you express a number in terms of the product of its prime factors, then it is called prime factorization. For example, if we again take the example of the number 48 and express it as 2×2×2×2×3, then this product of its prime factors (2 and 3) can be called its prime factorization. Now let's solve some examples so that you can grasp them completely.
Example: Find the prime factorisation of the number 30
Solution: 30 in terms of its prime factorisation can be written as 2×3×5. Here, we can see that the prime factors of the number 30 are 2, 3 and 5.
Example: Find the prime factorisation of the number 72
Solution: The prime factorisation of the number 72 is 2×2×2×3×3 with 2 and 3 being the prime factors of 72.
Example: Find the prime factorisation of the number 130
Solution: The number 130 can be written as 2×5×13 which will be its prime factorisation. Here, the numbers 2, 5 and 13 are the prime factors of 130.
So, this was all about Factors of 48, its prime factorisation, etc. We have provided enough examples to let you understand this topic. If you are still not able to understand this topic, you can refer to online video lectures for Maths or Maths NCERT books which will help you to understand this properly. You can find both of these resources on the Vedantu website or the Vedantu app.
Prime Factorization of 48
According to the prime factor definition we know that the prime factor of a number is the product of all the factors that are prime ( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of 48.Or the other way to find the prime factorization of 48 is by prime factorization or by factor tree. We know all the factors of 48, so the sum of all factors of 48 is –Prime factors -1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
Therefore, the sum of all factors of 48 is 124. Prime Factor of any Prime Number:For example let’s find the prime factor of 41:To make the task easier we can find the square root of the given number. Let’s suppose that 41 is not a prime number, then the number would be divisible by at least one prime number which is less than or equal to the square root of the number √41 ≈ 6.4. Now, list all the prime numbers less than 6 which are 2,3 and 5 and since 41 cannot be divided evenly by 2, 3, or 5, we can conclude that 41 is a prime number. So there are no prime factors of 41.
Solved Examples
Example 1: Write down the factors of 48.
Solution) 48 ÷ 1 = 48
48 ÷ 2 = 24
48 ÷ 3 = 16
48 ÷ 4 = 12
48 ÷ 6 = 8
48 ÷ 8 = 6
48 ÷ 12= 4
48 ÷ 16 = 3
48 ÷ 24 = 2
48 ÷ 48 = 1
Therefore the factors of 16 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Example 2: Write down the factors of 68.
Solution: 68 ÷ 1 = 68
68 ÷ 2 = 34
68 ÷ 4 = 17
68 ÷ 17 = 4
68 ÷ 34 = 2
68 ÷ 68 = 1
Therefore the factors of 16 are 1, 2, 4, 17, 34 and 68.
FAQs on Factors of 48
1. What are the Factors of 48 and What are the Factors of 416?
Let’s discuss what are the factors of 48.The positive Integer factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. When 48 is divided by the numbers 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 gives no remainder that is the remainder is zero.
The Factors of 416 are-
416 is a composite number in Mathematics.
The prime factorization of the number 416 can be written as 2 x 2 x 2 x 2 x 2 x 13, which can be written 416 = (25) x 13.
5 and 1 are the exponents in the prime factorization.
Factors of 416 can be listed as 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208 and 416.
2. What are the Prime Factors of 41?
To make the task easier we can find the square root of the given number. Let’s suppose that 41 is not a prime number, then the number would be divisible by at least one prime number which is less than or equal to the square root of the number √41 ≈ 6.4. Now, list all the prime numbers less than 6 which are 2,3 and 5 and since 41 cannot be divided evenly by 2, 3, or 5, we can conclude that 41 is a prime number. So there are no prime factors of 41.
If you want to find a factor of a number, you've to divide it with another number. If the first number is divisible by the second number then you can say that the second number is a factor of the first number. Let's take an example. When we divide 48 with 4, we get 12 as an answer which means 48 is divisible by 4 and hence, we can conclude that 4 is a factor of 48. On the other hand, if we divide the same number i.e., 48 with 7, we see that it is not divisible by 7. Therefore, in this case, we can say that 7 is not a factor of 48. This is how you find a factor of a number. Let's now discuss the Factors of 48 – Definition and Prime Factorization.
3. Is the number 48 a composite number or a prime number?
To check whether the number 48 is a prime number or a composite number, you have to find its Factors. If the number 48 has more than two factors ( 1 and 48), then it is a composite number. After factorising, you will find that the factors of the number 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. Therefore, the number 48 is composite as it has more than two factors.
4. What are the possible positive factor pairs of 48?
If the product of any two positive numbers is 48, then those two numbers will form a factor pair of 48. For example, if we multiply 12 with 4, we will get 48 as a result. Similarly, if we multiply 24 with 2, we will again get 48 as a result. Therefore, (12,4) and (24,2) will be two positive factor pairs of 48. All the possible positive factor pairs of 48 are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).
5. What are the possible negative Factor pairs of 48?
To find the possible negative factor pairs of 48, you have to multiply any two negative numbers and check whether their product is equal to 48 or not. If their product is equal to 48, then these two negative numbers will form a negative factor pair of 48. For example, if we multiply (-1) with (-48), we will get 48 as an answer which means (-1, - 48) will form a negative factor pair of 48. Doing all the calculations, the possible negative pair factors of 48 come out as (-1, -48), (-2, -24), (-3, -16), (-4, -12), and (-6, -8).
