Examples of Divisors
As we already discussed in number theory, divisors are those positive integers that can evenly divide into another natural number without leaving a remainder. In other words, if you have an integer “n,” its divisors are the integers that, when multiplied by another integer, result in “n” without a remainder. Some examples of divisors for various natural numbers are discussed as below:
Divisors of 60
A number is a divisor of 60 if it divides 60 completely. Thus, x is a divisor of 60 if 60 divided by x is an integer. We have:
|
60/1 = 60 |
Pair 1: 1, 60 |
|---|---|
|
60/2 = 30 |
Pair 2: 2, 30 |
|
60/3=20 |
Pair 3: 3, 20 |
|
60/4=15 |
Pair 4: 4, 15 |
|
60/5=12 |
Pair 5: 5, 12 |
|
60/6=10 |
Pair 6: 6,10 |
Thus all the divisors for 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. So, it is concluded that 60 has a total of twelve divisors.
Divisors of 72
A number is a divisor of 72 if it divides 72 completely. Thus, x is a divisor of 72 if 72 divided by x is an integer. We have:
|
72/1 = 70 |
Pair 1: 1, 70 |
|---|---|
|
72/2 = 36 |
Pair 2: 2, 36 |
|
72/3 = 24 |
Pair 3: 3, 24 |
|
72/6 = 12 |
Pair 4: 6, 12 |
|
72/8 = 9 |
Pair 5: 8, 9 |
Thus all the divisors for 60 are 1, 2, 3, 4, 6, 8, 9, 12, 24, 36 and 72. So, it is concluded that 60 has a total of eleven divisors.
Divisors of 18
A number is a divisor of 18 if it divides 18 completely. Thus, x is a divisor of 18 if 18 divided by x is an integer. We have
|
18/1 = 18 |
Pair 1: 1, 18 |
|---|---|
|
18/2 = 9 |
Pair 2: 2, 9 |
|
18/3 = 6 |
Pair 3: 3, 6 |
|
18/6 = 3 |
Pair 4: 6, 3 |
Thus all the divisors for 60 are 1, 2, 3, 6, 9 and 18. So, it is concluded that 18 has a total of six divisors.
Some other examples of divisors includes:
- The divisors of 12 are 1, 2, 3, 4, 6, and 12.
- The divisors of 20 are 1, 2, 4, 5, 10, and 20.
- The divisors of 7 are 1 and 7.
- The divisors of 16 are 1, 2, 4, 8, and 16.
- The divisors of 25 are 1, 5, and 25.
- The divisors of 9 are 1, 3, and 9.
- The divisors of 1 are 1.
- The divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
- The divisors of 33 are 1, 3, 11, and 33.
- The divisors of 50 are 1, 2, 5, 10, 25, and 50.
Special Case: Divisors of Zero
All positive and negative integers are divisors of 0. This is because it can be evenly divided by any integer. In other words, any integer n divides 0 without leaving a remainder, so n is a divisor of 0. They are —4, —5, 0, 1, 2, 3, and so on.
Divisors in Maths
Divisor is the number from which we divide the dividend to determine the quotient and remainder. In arithmetic, division is one of the four fundamental operations; other operations are addition, subtraction, and multiplication.
Divisors in Number Theory are integers that divides another integer without leaving the remainder is also called a divisor.
In this article, we will discuss both definitions of a divisor, including the general, and the definition in number theory. We will also explore various properties and examples related to divisors and discuss concepts such as prime divisors, the number of divisors, the sum of divisors, and the difference between a divisor and a factor.
Table of Content
- What are Divisors?
- Properties of Divisors
- Divisors and Dividends
- Divisor in Number Theory
- Examples of Divisors
- What are Prime Divisors?
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