Divisibility By 5

Introduction

Before uncovering the divisibility rule by 5, let’s understand what the general divisibility rule is. For the divisibility rule to exist, the last digit of a number must be analyzed. Just by looking at it, without actually dividing it, there should be a certainty that a particular divisor can be able to divide a number.

It is obvious that even numbers cannot divide odd numbers and odd numbers cannot divide even numbers. For an even number to be divisible, it can be divided by 2 until the point that the remainder is 0. For an odd number to be divisible, it can be divided by a particular odd number (3, 5, 7) until the point that the remainder is 0.

Divisible By 5

It is very easy to check if a number is divisible by 5. All we need to do is to check if the last digit of the given number is 0 or 5. If it is, then automatically, the number is said to be divisible by 5.

The divisibility rule of 5 states that if any number, particularly in the unit place is 0 or 5, that number is divisible by 5. For example, 

• 335 has the last digit, 5 therefore it is divisible by 5.
• 330 has the last digit, 0 therefore it is divisible by 5.
• 332 has the last digit, 2 therefore it is not divisible by 5.
• 338 has the last digit, 8 therefore it is not divisible by 5.

This rule is mainly used for large numbers. This is because the outcome can be predicted without even carrying out the division. The last digit of the number says it all.

How Many Two-digit Numbers Are Divisible By 5?

For us to know how many two-digit numbers are divisible by 5, we need to do a little calculation using arithmetic progression or count the numbers sequentially.

In this case, we have to take up all the numbers that 5 can divide. Let’s look at the two methods.

Method 1: Counting the numbers sequentially.

Remember, we said two-digit numbers. If we didn’t, 5 would have been part of this sequence.

The two digits in sequential order are;

10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95.

Counting these numbers would sum up to 18. Therefore there are 18 two-digit numbers divisible by 5.

Method 2: Arithmetic progression.

In this method, 5 is the common difference that all of these numbers have therefore 5 is represented as (d). 10, which is the first number, is represented as (a) and 95 is represented as R.

This means that; 

a=10, d=5, R=95

Formula: 

R= a + (n – 1) d

(Imputing our values);

95= 10 + (n – 1) 5

n – 1 = 85/5

n – 1 = 17

n = 17 + 1

n = 18

From the two methods, we can see that it takes 18 two digits numbers to be divided by 5.

Numbers Divisible By 5

Any number that can be represented as a sum of tens is divisible by 5. The number that ends with 5 is also divisible by 5. This means that any number that ends with 0 and 5 can be divisible by 5.

Let’s make it more practical;

If 555 = 500 + 5

528 = 520 + 8

From the example, 555 is divisible by 5 because 550 and 5 are both divisible by 5. However, the number 528 is not divisible by 5. Note that 529 is divisible by 5 but 8 is not divisible by 5.

This simply means that for a number to be divisible by 5, the last digit of the number must be 0 or 5.

How Many Three-Digit Numbers Are Divisible By 5

To know a number that is divisible by 5, just like we have stated earlier, the number must be divisible by 5 or 0 in the unit area or placed in the number.

We are going to use the counting method to know how many three-digit numbers that can be divisible by 5.

The counting principle:

The counting principle states that a task can be done in two ways;

• One task can be done in x ways and the other in y ways. With this, the number of ways for the two tasks is XY.
• For either of the tasks, x or y, the number of ways it can be done is x + y.

We would use the counting principle to know how many three-digit numbers 5 can divide.

• The hundreds place: In this particular filling, 0 cannot fill it up. Therefore the number of ways the units can be filled is 9.
• The tens place: For the tens, the numbers can be filled in 10 ways only.
• The units place: Just like we said earlier, the units place can only have numbers 0 or 5. The number is divisible by 5 only if the units conform to this principle.

To know the solution, we need to multiply the three-digit numbers from the hundred, tens, and units. Which are 9×10×2=180

This means that 180 three-digit numbers are divisible by 5.

Conclusion

There are only two numbers that can be divisible by 5. The numbers are 0 and 5. This means that any number that does not end with 0 or 5 cannot be divided by 5. They are two-digit and three-digit numbers that can be divided by 5 as stated in this article.