Factors of 32 Using Prime Factorization
What are the Factors of 32?
If the number 32 is divided by a natural number such that the remainder is zero, then, this natural number is known as a factor of 32. In this case, the quotient obtained on division is also a factor of 32.
The factors of 32 are 1, 2, 4, 8, 16 and 32 because all these numbers divide the number 32 evenly.
Factors of 32 | Factor pairs of 32 | Prime Factorization of 32 |
|---|---|---|
1, 2, 4, 8, 16 and 32 | (1, 32), (2, 16), (4, 8) and (16, 2) | 2 x 2 x 2 x 2 x 2 |
The Factors of 32
Divisibility rules and division facts are applied to determine the factors of 32.
Divisor | Is the number a factor of 32? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 32 = 32 |
2 | Yes, 32 is even | 2 x 16 = 32 |
3 | No, 32 \(\div\) 3 = 10 R2 | - |
4 | Yes, 32 is even | 4 x 8 = 32 |
5 | No, the ones digit is not 0 or 5 | - |
6 | No, 32 \(\div\) 6 = 5 R2 | - |
7 | No, 32 \(\div\) 7 = 4 R4 | - |
8 | Yes, 32 is even | 8 x 4 = 32 |
9 | No, 32 \(\div\) 9 = 3 R5 | - |
If we continue the same way, we will notice that the number will repeat on reaching 16. Hence, we can stop checking the factor pairs after 9 as they begin to repeat.
So, the factors of 32 are 1, 2, 4, 8, 16 and 32.
[Note: If we divide 32 by 10, we get the quotient and remainder as 3 and 2, respectively. So, 10 is not a factor of 32. Similarly, you can check for other numbers as well.]
The Prime Factorization of 32
A natural number can be expressed as a product of prime numbers. These prime numbers are known as the prime factors of that natural number. This method of writing the multiplication of prime factors is known as prime factorization.
The prime factorization of 32 can be represented by using a factor tree as shown in the image.
So, the prime factorisation of 32 results in 2 x 2 x 2 x 2 x 2 = \(2^5\)
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Factor Pairs of 32
A factor pair of a number is a set of any two factors such that their product is the number itself.
The factor pairs of 32 are (1, 32), (2, 16)and (4, 8).
1 x 32 = 32
2 x 16 = 32
4 x 8 = 32
Positive factor pairs of 32.
This table represents the factor pairs in relation to 32 as the product of the factor pairs.
Positive Factors of 32 | Positive Factor Pairs of 32 |
|---|---|
1 x 32 | (1, 32) |
2 x 16 | (2, 16) |
4 x 8 | (4, 8) |
Solved Factors of 32 Examples
Example 1: How can we divide 32 chocolates between two students in a class?
Solution:
Since there are 32 chocolates available and these need to be distributed between 2 students, each student will receive \(\frac{32}{2}\) chocolates, or 16 chocolates.
As a result, each student will surely receive 16 chocolates.
Example 2: If each box of pens contains eight pens, how many pens are there in four boxes?
Solution:
According to the details provided in the question, each box contains 8 pens.
There are a total of 4 boxes, and hence, the total number of pens present in 4 boxes is 4 x 8 = 32.
This shows us that there are 32 pens in 4 boxes.
Example 3: What are the factors that both 32 and 72 have in common?
Solution:
The factors of 32 are 1, 2, 4, 8, 16, and 32, while the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
We can see that there are four common factors.
32 and 64 share four common factors: 1, 2, 4 and 8.
Example 4: How many different dimensions can a rectangle with an area of 32 square units have?
Solution:
The area of a rectangle is l x w, length times width. Each factor pair of 32 corresponds to the dimensions of the rectangle that has an area of 32 square units.
The factor pairs of 32 are (1, 32), (2, 16) and (4, 8). So the rectangle can have 3 different dimensions such that its area is 32 square units.
Composite numbers are numbers that have a factor other than 1 and themselves. Hence, composite numbers have more than two factors.
The division of any positive number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all positive numbers.