Divisibility Rule of 8
A number is said to be divisible by 8 if the remainder is zero and the quotient is a whole number. While smaller numbers can be easily checked for divisibility, there are certain rules to check the divisibility of larger numbers. These rules help us to check if a number is completely divisible by another number without actually doing the division. The divisibility rule of 8 states that a number will be divisible by 8 if its last three digits are either 000 or, they form a number that is divisible by 8.
What is the Divisibility Rule of 8?
According to the divisibility rule of 8, if the last three digits of a given number are zeros or if the number formed by the last three digits is divisible by 8, then such a number is divisible by 8. For example, in 4832, the last three digits are 832, which is divisible by 8. Therefore, the given number 4832 is completely divisible by 8. Similarly, in 7000, the last three digits are 000, which tells us that 7000 is divisible by 8.
Divisibility Rule of 8 for Large Numbers
Divisibility rules make the process of division quicker and easier. While the divisibility check for smaller numbers can be done easily, the rules are helpful for larger numbers. For example, to check if 31,000 is divisible by 8, we check the last three digits of the given number, which are 000. According to the divisibility rule of 8, we conclude that the given number 31,000 is divisible by 8. In other words, 31,000 passes the divisibility test of 8. Let us take another example of the number 354416. In this case, the last three digits are 416, which is divisible by 8. Therefore, 354416 is divisible by 8.
Divisibility Rule of 8 and 9
Testing the divisibility by 8 is simple since we just need to consider the last three digits of the given number. However, the divisibility rule of 9 is different from this but similar to the rule of 3. A number is divisible by 9 if the sum of all its digits is a multiple of 9. For example, let us check if 75816 is divisible by 8 and 9. Since the last three digits of the given number are 816, which is divisible by 8, therefore, the given number is divisible by 8. Now, let us check its divisibility by 9. The sum of the numbers is 7 + 5 + 8 + 1 + 6 = 27. Since 27 is divisible by 9, therefore, the given number 75816 is divisible by 9.
Divisibility Test of 8 and 11
We have seen that the divisibility test of 8 is checked by considering the last three digits of the given number. However, the divisibility test for 11 is different. If the difference of the sums of the alternate digits is either zero or divisible by 11, then the number is divisible by 11. Let us check if 86416 is divisible by 8 and 11. The last three digits of the number are 416, which is divisible by 8. Therefore, the number 86416 is divisible by 8. Now, let us check its divisibility by 11 by using the following steps:
 Step 1: Calculate the sum of the alternate numbers starting from the right. In this case, it is: 6 + 4 + 8 = 18.
 Step 2: After this, calculate the sum of the remaining alternate digits, 1 + 6 = 7.
 Step 3: Now, find the difference between the sums: 18  7 = 11. Since 11 is divisible by 11, the given number 86416 is also divisible by 11.
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Divisibility Rule of 8 Examples

Example 1: From the following set of numbers, select and write the numbers which are divisible by 8, using the divisibility test of 8.
3458, 432000, 7856
Solution:
a) In 3458, the last three digits are 458, which is not divisible by 8. Therefore, 3458 is not divisible by 8.
b) In 432000, the last three digits are 000. Therefore, 432000 is divisible by 8.
c) In 7856, the last three digits are 856, which is divisible by 8. Therefore, 7856 is divisible by 8.

Example 2: Observe the following statements and write true or false using the divisibility rule of 8.
a) 2000 is divisible by 8.
b) 1824 is not divisible by 8.
c) 14238 is not divisible by 8.
Solution:
a.) True. In 2000, the last three digits are 000. Therefore, 2000 is divisible by 8.
b.) False. In 1824, the last three digits are 824, which is divisible by 8. Therefore, 1824 is divisible by 8.
c.) True. In 14238, the last three digits are 238, which is not divisible by 8. Therefore, 14238 is not divisible by 8.

Example 3: Check whether 456788 is divisible by 8 or not.
Solution:
Using the divisibility rule of 8, in 456788, the last three digits are 788, which is not divisible by 8. Therefore, 456788 is not divisible by 8.
FAQs on Divisibility Rule of 8
What is the Divisibility Rule of 8?
The divisibility rule for 8 states that if the last three digits of a given number are zeros or if the number formed by the last three digits is divisible by 8, then such a number is divisible by 8. For example, in 1848, the last three digits are 848, which is divisible by 8. Therefore, the given number 1848 is completely divisible by 8.
Using the Divisibility Rule of 8, Check if 2328 is Divisible by 8?
Using the divisibility rule of 8, we can see that the last three digits of 2328 are 328 which is divisible by 8. Hence, 2328 is divisible by 8.
What is the Divisiblity Rule of 8 and 9?
The divisibility rule of 8 states that if the last three digits of the given number are zeros or they form a number that is divisible by 8, then the given number is divisible by 8. The divisibility rule of 9 says that a number is divisible by 9 if the sum of its digits is divisible by 9.
Using the Divisibility Test of 8, Check if 1000 is Divisible by 8?
Using the divisibility test of 8, we can see that the last three digits of 1000 are 000. This means that 1000 is divisible by 8.
How do you Know if a Big Number is Divisible by 8?
In order to check the divisibility for larger numbers, we need to check the last three digits of the given number. If the last three digits of a large number are zeros or a number that is divisible by 8, then the given number is said to be divisible by 8. For example, to check if 51,848 is divisible by 8, we check the last three digits of the given number, 848, which is divisible by 8. Hence, we can say that 51,848 is divisible by 8.
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