Factors of 28 Using Prime Factorization
What are the Factors of 28?
Factors are numbers that can divide 28 completely. When two factors are multiplied together to produce the number 28 they are said to be factor pairs. It is important to remember that these factors divide the number completely. As a result, fractions cannot be used.
Factors of 28 are 1, 2, 4, 7, 14, and 28.
The factorization method is used to find the factors of the number 28.
How can we Calculate Factors of 28?
We have to divide 28 by all natural numbers from 1 to 28 to find its factors as all natural numbers will not divide 28 completely. Here are some numbers which do not leave a remainder when 28 is divided by them:
- 28 ÷ 1 = 28
- 28 ÷ 2 = 14
- 28 ÷ 4 = 7
- 28 ÷ 7 = 4
- 28 ÷ 28 = 1
Finding Prime Factors of 28 using a Factor Tree
28 is a composite number that should have prime factors. Let’s look at how to find the prime factors of 28:
- The first step is to divide 28 by the smallest prime factor, which is 2.
28 ÷ 2 = 14
- Again divide 14 by 2 and the process goes on.
14 ÷ 2 = 7
- Now, dividing 7 by 2 yields a fractional number, which isn’t a factor. So, let’s move onto the next set of prime numbers. Dividing 7 by 3 and 5 would again give us a fractional result. The next prime number is 7 and in this case it would not be a fraction. This can be seen as
7 ÷ 7 = 1
- At the end of the division process, we find the number one. This means that we need not go any further.
As a result, the prime factors of 28 are 2 \( \times \) 2 \( \times \) 7 or 2\( ^2 \times \)7, where 2 and 7 are prime numbers.
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Factor pairs of 28
To find the factor pairs, multiply two numbers in a pair to get a product of 28. Examples of such pairs are:
Positive factors of 28 | Positive factor pairs of 28 |
|---|---|
1 × 28 | (1, 28) |
2 × 14 | (2, 14) |
4 × 7 | (4, 7) |
- 1 × 28 = 28, (1, 28) is a factor pair of 28.
- 2 × 14 = 28, (2, 28) is a factor pair of 28.
- 4 × 7 = 28, (4, 28) is a factor pair of 28.
Hence, the positive factor pairs are (1, 28), (2, 14), and (4, 7).
Solved Factors of 28 Examples
Example 1: Find the number of the common factors shared by 36 and 28.
Solution:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 36
Factors of 28: 1, 2, 4, 7, 14, and 28.
So, the common factors of 36 and 28 are 1, 2, and 4.
Hence, 28 and 36 have 3 common factors.
Example 2: On a table, there are 28 chocolates. Jane is responsible for distributing the chocolates equally to her four friends. What is the total number of candies that each friend will receive after the distribution is done?
Solution:
Total number of chocolates = 28
Total number of friends = 4
Number of chocolates, each child will get \( \frac{28}{4} \) or 7.
So, each friend of Jane will have 7 chocolates after the distribution is done.
Example 3: List out the factors of 28 and its factor pairs.
Solution:
All the combinations of the two factors multiplied together to give a result of 28 are known as the factor pairs of 28.
Factors of 28: 1, 2, 4, 7, 14, and 28.
1 × 28 = 28
2 × 14 = 28
7 × 4 = 28
Hence, the factor pairs of 28 are (1, 28), (2, 14) and (4, 7).
No, 9 is not a factor of 28 as the number 9 does not divide 28 exactly. After the division it leaves behind a remainder of 1. So, 9 is not a factor of 28.
Factors of 14 are 1, 2, 7, and 14, and the factors of 28 are 1, 2, 4, 7, 14, and 28.
So, the common factors of 14 and 28 are 1, 2, 7, and 14.
As we know, the prime factors of 28 are 2 × 2 × 7. As a result, the prime factor with the greatest numerical value is 7.
Yes, 28 is a composite number as it has factors other than 1 and itself. The other factors of the number 28 are 2, 4, 7, and 14.
The following are some important properties of factors:
- Any number’s exact divisor is called its factor.
- Every number has a common factor in 1.
- All the factors of a number should always be less than or equal to the number itself.
- The greatest factor of a number is the number itself.