Factors of 27 Using Prime Factorization
- What are the Factors of 27?
- Factor List for Number 27
- Explaining the Prime Factors of 27
- Factor Pairs of 27
- Rapid Recall
- Solved Examples
- Frequently Asked Questions
What are the Factors of 27?
The factors of 27 are those numbers that divide 27 without leaving any remainder. Or we can say that the factors of 27 will divide it in an equal manner.
The factors of 27 can be positive as well as negative. But the factors of 27 cannot be a decimal or a fraction.
Factors of 27:
Factors | Pair factors | Prime factors |
|---|---|---|
1, 3, 9, 27 | (1, 27), (3, 9) | 27 = 3 x 3 x 3 |
Factor List for Number 27
Divisor | Is the number a factor of 27? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 27 = 27 |
2 | No, 27 is an odd number. | - |
3 | Yes, 2 + 7 = 9, 27 is divisible by 3 | 3 x 9 = 27 |
4 | No, 27 is odd. | - |
5 | No, ones digit of 27 is 7 | - |
6 | No, 27 is odd. | - |
7 | No, 27 \(\div\) 7 = 3and leaves a remainder of 6. | - |
8 | No, 27 is odd. | - |
9 | Yes, 27 \(\div\) 9 = 3 | 9 x 3 = 27 |
27 | Yes, 27 \(\div\) 27 = 1 | 27 x 1 = 27 |
Hence, the factors of 27 are 1, 3, 9 and 27.
Explaining the Prime Factors of 27
The number 27 is a composite number. It indicates that 27 as a number has more than one factor other than one and itself.
We can represent the factors of 27 with the help of a factor tree. This factor tree can also be used to learn about the prime factorization of 27.
From the factor tree we can observe that the prime factorization of 27 is 3 × 3 × 3.
This shows us that 3 is the only prime factor of 27.
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Factor Pairs of 27
The factor pair of 27 is the combination of two factors of 27 which when multiplied together lead to 27 as the product.
Hence the factors of 27: 1, 3, 9 and 27.
All the combination of two factors multiplied together to give a result of 27 is known as factor pairs of 27.
Positive factors of 27 | Positive factor pairs of 27 |
|---|---|
1 x 27 | (1, 27) |
3 x 9 | (3, 9) |
Rapid Recall
Solved Factors of 27 Examples
Example 1: Find the common factors of 20 and 27.
Solution:
Factors of 27: 1, 3, 9, 27
Factors of 20: 1, 2, 4, 5, 10, 20.
So, the common factors of 20 and 27 are only number 1.
Hence, 20 and 27 have 1 common factor.
Example 2: John has three boxes. Also, he has some blue, red and orange marbles. Can he arrange an equal number of marbles in each box?
Marbles | Number of marbles |
|---|---|
Oranges | 8 |
Red | 10 |
Blue | 9 |
Solution:
Step 1: Add to find out total number of marbles
8 + 10 + 9 = 27 [Add]
So, John has 27 marbles.
Step 2: Check if the total number of marbles is divisible by the number of boxes.
27 is divisible by 3 as 3 is a factor of 27.
27 \(\div\) 3 = 9 Using the factor pair (3, 9)
Hence, John can arrange an equal number of 9 marbles in each box.
Example 3: How many factor pairs of number 27 exist?
Solution:
All the combination of two factors multiplied together to give a result of 27 is known as factor pairs of 27.
Factors of 27: 1, 2, 3, and 27.
Factor pairs of 27 are (1, 27), (3, 9)
Hence, the number 27 has a total of 2 factor pairs.
Frequently Asked Questions on Factors of 27
Yes, 9 is a factor of 27. As the number 9 divides 27 exactly. It leaves 0 as the remainder. So, 9 is a factor of 27.
Yes, 27 is a composite number as it has factors other than one and itself. It has factors such as 3 and 9 other than 1 and 27.
The factors of 27 are 1, 3, 9, 27.
So, the least factor of 27 is 1 and the greatest factor is 27 itself.
The factors of 27 are 1, 3, 9 and 27.
Hence, the sum of all the factors of 27 is
= 1 + 3 + 9 + 27
= 40
Hence, the sum is 40.
Factors of 27 are 1, 3, 9, and 27.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
So, the common factors of 27 and 24 are 1 and 3.
