Students can find the divisibility rules questions and answers, which will help them understand different divisibility rules. As we know, divisibility rules help to check if the number is completely divisible by a number without actually performing the division operation. Here, we have offered different divisibility questions with complete explanations of solutions to understand the concept easily. To learn more about divisibility rules, click here.
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What are Divisibility Rules? A divisibility rule enables us to know whether a particular number is divisible by a divisor simply looking at its digits instead of going through the complete division operation. It allows us to determine multiples and factors of numbers without undergoing the long division operation. By using divisibility rules, a person can determine whether an integer is divisible by another integer. Also, check: Divisibility Rule of 3. |
Divisibility Rules Questions with Solutions
1. Check whether 1440 is divisible by 15.
Solution:
Given number = 1440.
Now, we need to check whether the number 1440 is divisible by 15.
According to the divisibility rule of 15, a numeral is divisible by 15 if it is divisible by both 3 and 5.
Since the unit digit of 1440 is 0, it is divisible by 5.
Also, the sum of digits of 1440 = 1 + 4 + 4 + 0 = 9
Hence, the sum of digits is 9, it is divisible by 3.
Since 1440 is divisible by both 3 and 5, 1440 is divisible by 15.
2. Is 2848 divisible by 11?
Solution:
The given number is 2848.
To check whether the number 2848 is divisible by 11, follow the below steps:
Step 1: First, find the sum of alternative digits.
It means,
2 + 4 = 6
8 + 8 = 16
Step 2: Find the difference between 6 and 16.
The difference between 6 and 16 = 16 – 6 = 10.
Step 3: Check whether the difference value obtained in step 2 is divisible by 11 or not.
Here, the difference = 10, which is not divisible by 11.
Therefore, 2848 is not divisible by 11.
3. How many three-digit numbers are divisible by 5?
Solution:
As we know, the sequence of three-digit numbers that are divisible by 5 is:
100, 105, 110, 115, 120, …995.
Therefore, we can say that the given sequence is in Arithmetic Progression with the first digit being 100 and the common difference being 5.
i.e, a = 100, d = 5 and nth term = 995
Now, we need to find the number of three-digit numbers that are divisible by 5.
Therefore,
995 = 100 + (n-1)5
995 = 100 + 5n – 5
995 = 95 + 5n
5n = 995 – 95
5n = 900
Therefore, n = 900/5 = 180.
Therefore, the number of 3-digit numbers that are divisible by 5 is 180.
4. Check whether the number 2024 is divisible by 4.
Solution:
Given number: 2024.
As we know, a number is divisible by 4, if the last two digits of the given number are exactly divisible by 4.
In the given number 2024, the last 2 digits are 24.
Here, 24 is completely divisible by 4.
i.e., 24/4 = 6.
Therefore, 2024 is divisible by 4.
5. Is 119 divisible by 7?
Solution:
Given number: 119.
Using the divisibility rule of 7, let’s check whether 119 is divisible by 7 or not.
Step 1: Multiply the last digit of 119 by 2.
Here, we get 9 × 2 = 18
Step 2: Now, subtract 18 from 11, and we get -7.
Since -7 is a multiple of 7, we can say 119 is divisible by 7.
Therefore, 119 is divisible by 7.
6. Is 99992 divisible by 8?
Solution:
Given number: 99992.
According to the divisibility rule of 8, a number is divisible by 8 if the last three digits of a number are divisible by 8.
In the number 99992, the last 3 digits are 992.
Now, we need to check whether 992 is divisible by 8.
When 992 is divisible by 8, we get the quotient as 124 and the remainder as 0.
So, 992 is divisible by 8.
Therefore, 99992 is divisible by 8.
7. Check whether the number 2112 is divisible by 6?
Solution:
The given number is 2112.
As we know, the number is divisible by 2 and 3, and then the number is divisible by 6.
In the given number 2112, the last digit is an even number, i.e. 2, and hence the number 2112 is divisible by 2.
Also, the sum of digits of 2112 is divisible by 3, and hence 2112 is divisible by 3.
i.e., 2 + 1 + 1 + 2 = 6, which is divisible by 3.
Hence, we can say that the number 2112 is divisible by 6.
8. Check whether 4355 is divisible by 13?
Solution:
Given number: 4355
To check whether the given number is divisible by 13, follow the below steps:
Step 1: Multiply the unit digit of the given number by 4.
i.e. 5 × 4 = 20
Step 2: Now add the product obtained in step 1 with the remaining digits of the given number.
i.e., 20 + 435 = 455
Step 3: Repeat step 1 and step 2, until we get the two-digit number.
i.e, 45 + (5 × 4)
⇒ 45 + 20
⇒ 65
Hence, 65 is divisible by 13, and therefore we can conclude that 4355 is divisible by 13.
9. Is 783 divisible by 9?
Solution:
Yes, the number 783 is divisible by 9.
Explanation:
To check whether 783 is divisible by 9, add all the digits of the given number. If the sum value is divisible by 9, then the given number should be divisible by 9.
i.e., 7 + 8 + 3 = 18.
18 is divisible by 9.
Therefore, 783 is divisible by 9.
10. Check whether 10032 is divisible by 12, and justify your answer.
Solution:
Yes, the number 10032 is divisible by 12.
Justification:
As we know, a number is divisible by 12 if it is divisible by both 3 and 4.
Now, we have to check the divisibility rule of 3 and 4 for the given number 10032.
Checking for Divisibility Rule of 3:
10032 = 1 + 0 + 0 + 3 + 2 = 6, which is divisible by 3.
Checking for Divisibility Rule of 4:
The last two digits of 10032 are 32, which is divisible by 4.
Hence, the number 10032 is divisible by both 3 and 4, we can say that the number 10032 is divisible by 12.
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Practice Questions
- Check whether the number 1744 is divisible by 8.
- Is 3245 divisible by 11?
- How many three-digit numbers are divisible by 9?
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