Factors of 135 Using Prime Factorization
The Factors of 135
A factor of a number is an integer that divides the number evenly, that is, leaving no remainder. The factors of a number can be determined using divisibility rules and division facts. Here, we will learn about the factors, prime factors, and factor pairs of 135.
The factors of 135 are those integers that divide 135 without leaving any remainder. In other words, we can say that the factors of 135 will divide it completely.
The factors of 135 can be positive as well as negative, but they cannot be decimals or fractions. The quotient obtained on dividing 135 by its factor is also a factor of 135.
Factors | Factor Pair | Prime Factorization |
|---|---|---|
1, 3, 5, 9, 15, 27, 45, 135 | (1, 135), (3, 45),(5, 27) (9, 15) | 135 = 3 × 3 x 3 x 5 |
For example, 5 is a factor of 135 because on dividing 135 by 5, it leaves 0 as the remainder and 27 as the quotient, which is also a factor of 135.
Factor List for the Number 135
Divisor | Is the number a factor of 135? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 × 135 = 135 |
2 | No, 135 is odd | - |
3 | Yes, 1 + 3 + 5 = 9, 135 is divisible by 3 | 3 × 45 = 135 |
4 | No, 135 ÷ 4 = 33 Remainder = 2 | - |
5 | Yes, 135 ÷ 5 = 27 Remainder = 0 | 5 × 27 = 135 |
6 | No, 135 is odd | - |
7 | No, 135 ÷ 7 = 19 Remainder = 2 | - |
8 | No, 135 is odd | - |
9 | Yes, 135 ÷ 9 = 15 Remainder = 0 | 9 × 15 = 135 |
Therefore the factors of 135 are: 1, 3, 5, 9, 15, 27, 45, and 135
The Prime Factors of 135
A factor tree can be used to determine the prime factors of 135 as shown in the image.
From the factor tree, we can see that the prime factorization of 135 is 3 x 3 x 3 x 5 = \(3^3\) x 5.
This means 3 and 5 are the prime factors of 135.
Read More:
The Factor Pairs of 135
The factor pair of any number is a set of two numbers either positive or negative that, when multiplied, result in that number. So, the two numbers are factors of the number. A factor pair can be negative or positive.
[Note: The product of two negative numbers is positive.]
The factor pair of 135 is a set of two factors of 135 that, when multiplied, give 135 as the product.
Thus, the factor pairs of 135 can be obtained from the list of its factors.
Positive Factors of 135 | Positive Factor Pair of 135 |
|---|---|
1 x 135 | (1, 135) |
3 x 45 | (3, 45) |
5 x 27 | (5, 27) |
9 x 15 | (9, 15) |
Rapid Recall
Recalling the factors of 135 can be made easy with this image:
Solved Factors on 135 Examples
Example 1: 3 classes are going on a field trip. The classes will use 2 buses. Can the teachers have an equal number of students on each bus?
Class | Students |
|---|---|
1 | 40 |
2 | 60 |
3 | 35 |
Solution:
Step 1: Add to find out the number of students who are going on the field trip.
40 + 60 + 35 = 135 [Add]
So, 135 students are going on the field trip.
Step 2: Is the total number of students divisible by the number of buses?
Since the number 135 is an odd number.
So, 135 is not divisible by 2.
Hence, the teachers do not have an equal number of students on each bus.
Example 2: Find the common factors of 192 and 135.
Solution:
The factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.
The factors of 135: 1, 3, 5, 9, 15, 27, 45, and 135.
So, the common factors of 135 and 192 are 1 and 3.
Hence, 196 and 135 have 2 common factors.
Example 3: What are the common factors of 135 and 168?
Solution:
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
So, the common factors of 135 and 168 are 1 and 3.
Yes, 9 is a factor of 135 as the number 9 divides 135 exactly. It leaves the remainder 0. So, 9 is a factor of 135.
Yes, 135 is a composite number as it has factors other than 1 and itself, that is, 135. In other words, the number 135 has more than two factors.
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.
So, the smallest factor of 135 is 1, and the greatest factor is 135 itself.
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135
Hence, the sum of the all the factors of 135 is
= 1 + 3 + 5 + 9 + 15 + 27 + 45 + 135 = 240
Hence, the sum is 240.
The factors of 135: 1, 3, 5, 9, 15, 27, 45, and 135. So, there are 8 factors of 135.