Divisibility rule of 5 is a simple rule to determine whether a number can be divided by 5 without leaving a remainder. This rule simplifies the process of determining whether a number can be divided by 5 without leaving a remainder. Knowing the divisibility rule of 5 helps in quick calculations, enhances problem-solving skills, and forms a fundamental part of number theory and arithmetic. This article will explore the details of the divisibility rule of 5, and its applications, and provide clear examples to ensure a thorough understanding.

What is the Divisibility Rule?

Divisibility rule is a shortcut or a set of guidelines that helps determine whether a given number can be divided by another number without actually performing the division. These rules simplify the process of checking for divisibility by using specific properties of numbers.

Divisibility rules typically exist for specific divisors, such as 2, 3, 4, 5, 6, 9, 10, etc.

For example:

• The divisibility rule for 2 states that if the last digit of a number is even (0, 2, 4, 6, or 8), then the number is divisible by 2.
• The divisibility rule for 3 states that if the sum of digits is divisible by 3, then the number is divisible by 5.
• The divisibility rule of 4 states that a number is divisible by 4 if the last two digits form a number that is divisible by 4.
• The divisibility rule of 7 states that a number is divisible by 7 if you double the last digit, subtract it from the rest of the number, and the result is divisible by 7.

What is Divisibility Rule of 5?

Divisibility rule or Divisibility test of 5 states that a number is divisible by 5 if its last digit is either 0 or 5. This means that when you look at the units place (the rightmost digit) of the number, it must be a 0 or a 5 for the number to be evenly divisible by 5.

A number is divisible by 5 if its last digit is either 0 or 5.

By using this rule, we can easily check the divisibility of any number by 5. It helps to determine the divisibility by 5 without performing long division.

Examples of Divisibility Rule of 5

We can easily determine whether a number is divisible by 5 by simply examining its last digit. Few Examples for the same are:

• 35: The last digit is 5, so 35 is divisible by 5.

• 80: The last digit is 0, so 80 is divisible by 5.

• 123: The last digit is 3, so 123 is not divisible by 5.

• 450: The last digit is 0, so 450 is divisible by 5.

Divisibility Rule of 5 for Large Numbers

The divisibility rule of 5 is particularly straightforward and remains effective regardless of the size of the number. The rule states that a number is divisible by 5 if its last digit is either 0 or 5. This test applies to both small and large numbers. We have to follow these simple steps:

• Identify the Last Digit: Look at the last digit of the number.
• Apply the Rule:
  • If the last digit is 0 or 5, the number is divisible by 5.
  • If the last digit is any other digit (1, 2, 3, 4, 6, 7, 8, 9), the number is not divisible by 5.

Let us consider an example to check the divisibility by 5 for larger numbers:

Example: Check the divisibility by 5 for the number 123,456,780.

Solution:

Given number: 123,456,780

Last digit of the number is 0

Hence 123,456,780 is divisible by 5.

Divisibility Rule of 5 and 10

As we have already studied about divisibility rule of 5 which states “that a number is divisible by 5 if its last digit is either 0 or 5”.

Similarly, Divisibility rule of 10 states that a number is divisible by 10 if its last digit is 0. This rule is also straightforward and easy to apply.

Let us take a few examples for the same:

Example 1: Check if the number 225 divisible by 5 and 10?

Solution:

Given Number: 225

• Last digit: 5
• Divisibility by 5: Yes, 25 is divisible by 5.
• Divisibility by 10: No, 25 is not divisible by 10.

Example 2: Check if the number 4730 divisible by 5 and 10?

Solution:

Given Number: 4730

• Last digit: 0
• Divisibility by 5: Yes, 4730 is divisible by 5.
• Divisibility by 10: Yes, 4730 is divisible by 10 also.

Hence, we can say that if the last digit of a number is zero(0), then it is divisible by both 5 and 10.

How to Find Numbers Divisible By 5?

Numbers divisible by 5 are those that end in either 0 or 5. This applies to numbers of any length and simplifies the process of checking divisibility. There are infinite numbers which are divisible by 5, however we can determine how many numbers are divisible by 5 between 1 and a given number ‘n’ by the formula:

Count = n/5

For Example: To calculate number between 1 and 100 we will use the above formula:

Count = n/5

Here n = 100

Count = 100/5 = 20

Hence there are 20 numbers between 1 and 100 that are divisible by 5.

Related Articles:

Factors of a Number	Divisibility Rule of Four	Divisibility Rule of 11	Integers
Divisibility Rule of 13	Divisibility Rules From 1 to 19	Divisor	Whole Numbers

Solved Examples on Divisibility Rule of 5

Example 1: Is the number 2460 divisible by 5?

Solution:

Given number is 2460

• Identify the last digit of the number.
• The last digit of 2460 is 0.
• Since the last digit is 0, 2460 is divisible by 5.

Example 2: Use the divisibility rule of 5 to check the divisibility of 789 by 5?

Solution:

Given number: 789

• Identify the last digit of the number.
• The last digit of 789 is 9.
• Since the last digit is not 0 or 5, 789 is not divisible by 5.

Example 3: Is the number 5805 divisible by 5?

Solution:

Given number is 5805

• Identify the last digit of the number.
• The last digit of 5805 is 5.
• Since the last digit is 5, 5805 is divisible by 5.

Example 4: Find the largest 4-digit number divisible by 5.

Solution:

To find the largest 4-digit number divisible by 5, we need to consider the largest possible 4-digit number and then find the largest one that is divisible by 5.

The largest 4-digit number is 9999.

To find the largest 4-digit number divisible by 5, we need to find the largest multiple of 5 that is less than or equal to 9999.

The largest multiple of 5 less than or equal to 9999 is 9995.

So, the largest 4-digit number divisible by 5 is 9995.

Practice Questions on Divisibility Rule of 5

Here are some practice questions on the divisibility rule of 5 for you to solve:

Q1: Determine whether the following numbers are divisible by 5:

• a) 420
• b) 287
• c) 875
• d) 900
• e) 333

Q2: Find the smallest 3-digit number divisible by 5.

Q3: How many numbers between 100 and 200 are divisible by 5?

Conclusion

By applying this simple rule, we can easily check whether a number is divisible by 5 without performing any complex calculations. Just look at the last digit of the number:

• If it is 0 or 5, the number is divisible by 5.
• If it is any other digit, the number is not divisible by 5.

Divisibility Rule of 5 – FAQs

How many three-digit numbers are divisible by 5?

To find out how many three-digit numbers are divisible by 5, we need to count the multiples of 5 within the range of three-digit numbers.

• The first three-digit multiple of 5 is 100, and the last three-digit multiple of 5 is 995.
• To find multiples of 5 between 100 and 995 we divide the difference (995 – 100 = 895) by 5 and add 1. So, 895/5 + 1 = 179 + 1 = 180.
• Therefore, there are 180 three-digit numbers divisible by 5.

How many two digits numbers are divisible by 5?

To find out how many two-digit numbers are divisible by 5, we need to count the multiples of 5 within the range of two-digit numbers, which is from 10 to 99.

• The first two-digit multiple of 5 is 10, and the last two-digit multiple of 5 is 95.
• To find multiples of 5 between 10 and 95 we divide the difference (95 – 10 = 85) by 5 and add 1. So, 85/5 + 1 = 17 + 1 = 18.
• Therefore, there are 18 two-digit numbers divisible by 5.

What number is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10?

The smallest number that is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 is 2520.

What is the divisibility test of 5?

The divisibility test of 5 states that a number is divisible by 5 if its last digit is either 0 or 5.

Is there a similar rule for divisibility by 10?

Yes, there is a similar rule for divisibility by 10. A number is divisible by 10 if its last digit is 0.

How to quickly check if a large number is divisible by 5?

To quickly check if a large number is divisible by 5, you only need to look at its last digit. If the last digit is 0 or 5, then the number is divisible by 5.