Factor of 48 Using Prime Factorization
What are the Factors of 48?
The factors of 48 are natural numbers that divide it completely. Alternatively, we can view factors of 48 as numbers that can be multiplied by another number to get 48 as the product. We won’t get a remainder if we divide 48 by any of its factors. On the other hand, we will get a remainder if we divide 48 by a number that is not its factor. The factors of 48 are given below.
Factor list of 48
Divisibility rules and division facts can be used to obtain the factors of 48.
Divisor | Is the number a factor of 48? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 48 = 48 |
2 | Yes, 48 is even | 2 x 24 = 48 |
3 | Yes, 4 + 8 = 12, which is divisible by 3 | 3 x 16 = 48 |
4 | Yes, 48 \(\div\) 4 = 12 R 0 | 4 x 12 = 48 |
5 | No, the ones digit is not 0 or 5. | - |
6 | Yes, 48 is even and divisible by 3 | 6 x 8 = 48 |
7 | No, 48 \(\div\) 7 = 6 R 6 | - |
8 | Yes, 48 \(\div\) 8 = 6R 0 | 8 x 6 = 48 |
We can stop the derivation of factors with this step because the multiplication equations will start to repeat. So, the factors of 48 are the multiplicands of each multiplication equation. Since there are 5 multiplication equations with unique multiplicands, the number 48 has ten factors, which are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Prime Factorization of 48
Prime factorization implies that we express a number as a product of prime numbers. The prime numbers multiplied here are known as the prime factors of the original number.
The factor tree of 48 below represents the prime factorization of 48.
So, the prime factorization of 48 is 2 x 2 x 2 x 2 x 3 and the prime factors of 48 are 2 and 3.
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Factor Pairs of 48
A factor pair of 48 is a set of any of its two factors whose product is 48. The factor pairs of a number can be written from the list of factors of that number.
The factor pairs of 48 are listed below.
Factors of 48 | Factor Pairs of 48 |
|---|---|
1 x 48 | (1, 48) |
2 x 24 | (2, 24) |
3 x 16 | (3, 16) |
4 x 12 | (4, 12) |
6 x 8 | (6, 8) |
Solved Factors of 48 Examples
Example 1: Find the common factors of 48 and 64.
Solution:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
The factors of 64 are 1, 2, 4, 8, 16, 32 and 64.
Hence, the common factors of 48 and 64 are 1, 2, 4, 8 and 16.
Example 2: Find the greatest common factor (GCF) of 48 and 96.
Solution:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.
So, the greatest common factor of 48 and 96 is 48.
Example 3: Flinn wants to share 48 chocolates among 9 of his friends. Is it possible to share the chocolates equally?
Solution:
Number of chocolates = 48
Number of friends = 9
For Flinn to be able to share the chocolates equally among his friends the number of chocolates should be evenly divisible by the number of friends.
But 9 is not a factor 48, that is, 48 is not evenly divisible by 9.
Therefore, Flinn will not be able to share 48 chocolates equally among 9 friends.
The number 48 has ten factors. They are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
The prime factorization of 48 gives us 2 x 2 x 2 x 2 x 3.
The factor pairs of 48 are (1, 48), (2, 24), (3, 16), (4, 12) and (6, 8).
When 48 is divided by 10 we get a remainder equal to 8. So 48 is not completely divisible by 10. Therefore 10 is not a factor of 48.