Factors of 26 Using Prime Factorization
What are the Factors of 26?
If the number 26 is divided by a natural number such that the remainder is zero, this natural number is known as a factor of 26. Here, the quotient obtained on division is also a factor of 26.
The factors of 26 are 1, 2, 13, and 26 because all these numbers divide the number 26 exactly.
List of the Factors of 26
Divisor | Is the number a factor of 26? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 x 26 = 26 |
2 | Yes, 26 is even. | 2 x 13 = 26 |
3 | No, 2 + 6 = 8 is not divisible by 3. | - |
4 | No, 26 \(\div\) 4 = 6 R2 | - |
5 | No, ones digit is neither 0 nor 5. | - |
6 | No, 26 is even but not divisible by 3. | - |
7 | No, 26 \(\div\) 7 = 3 R5 | - |
8 | No, 26 \(\div\) 8 = 3 R2 | - |
9 | No, 26 \(\div\) 9 = 2 R8 | - |
10 | No, 26 \(\div\) 10 = 2 R6 | - |
11 | No, 26 \(\div\) 11 = 2 R4 | - |
12 | No, 26 \(\div\) 12 = 2 R2 | - |
13 | Yes, 26 \(\div\) 13 = 2 R0 | 13 x 2 = 26 |
On reaching 13, we can see that the multiplication equations will start to repeat. So, we have now derived all the factors of 26.
Hence, the factors of 26 are 1, 2, 13, and 26.
Prime Factorization of 26
If a natural number can be expressed as a product of prime numbers, then, these prime numbers are known as the prime factors of that natural number. This process of expressing a number as the product of its prime factors is known as prime factorization.
The prime factorization of 26 can be represented by using a factor tree as shown in the image:
So, the prime factorization of 26 is 26 = 2 x 13 and the prime factors of 26 are 2 and 13.
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Factor Pairs of 26
A factor pair of 26 is a set of two factors of 26 whose product is 26. We can observe that 26 has just two factor pairs.
Positive factor pairs of 26
Positive Factors of 26 | Positive Factor Pairs of 26 |
|---|---|
1 x 26 = 26 | (1, 26) |
2 x 13 = 26 | (2, 13) |
Solved Factors of 26 Examples
Example 1: Find the common factors of 26 and 27.
Solution:
Factors of 26 = 1, 2, 13, and 26
Factors of 27 = 1, 3, 9, and 27
Therefore, the common factor of 26 and 27 is 1.
Example 2: Find the greatest common factor of 26 and 30.
Solution:
Factors of 26 = 1, 2, 13, and 27
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30
So, the common factors of 26 and 30 are 1 and 2.
Therefore, the greatest common factor of 26 and 30 is 2.
Example 3: Andrew wants to hang a rectangular photo frame in his room. The area available on the wall for hanging the frame is 26 cm\(^2\). Find the possible dimensions of the rectangular frame, if it is known that both the length and the width are integers and the frame completely utilizes the available space.
Solution:
The area available on the wall to hang the photo frame will be equal to the area of the rectangular photo frame which is 26 cm\(^2\).
We know that, area of a rectangle = length x width
26 = length x width
So, the dimensions of the frame will be the factor pairs of 26.
Therefore, the possible dimensions of the rectangular frame are:
Length (in centimeters) | Width (in centimeters) |
|---|---|
1 | 26 |
2 | 13 |
13 | 2 |
26 | 1 |
The factors of 26 are the numbers that divide 26 exactly, leaving the remainder as zero. 26 is exactly divisible by 1, 2, 13 and 26 only. So, the factors of 26 are 1, 2, 13 and 26.
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.
Composite numbers are those numbers which have factors other than 1 and themselves, that is, a composite number has more than two factors.
Factors of 26 = 1, 2, 13, and 26.
Sum of factors of 26 = 1 + 2 + 13 + 26 = 42
No, because one’s digit is neither 0 or 5. If we divide 26 by 5, we get the quotient as 5 and remainder as 1. So, as 26 divided by 5 results in a non-zero remainder, 5 is not a factor of 26.