 # Worksheet on Divisibility Rules | Divisibility Tests Worksheet PDF with Answers

Any number can be divided with precision using the simple rules named Divisibility Rules. Master the concept of dividing large numbers too in no time using the collection of printable worksheets on divisibility rules. Test your skills with the revision worksheets for divisibility tests and learn divisibility rules of various numbers. Factors of larger numbers can be found simply using the divisibility rules.

To enhance your proficiency in the math concept of divisibility there is no other way than to practice the problems on divisibility rules. Improve your analytical and problem-solving ability by answering the questions divisible by numbers 2-12 present here. 5th Grade Math Students can Download the Free Interactive Exercises on Divisibility Tests and practice anywhere and anytime.

Also, See: Properties of Divisibility

## Divisibility Worksheets with Answer Key

I. Which of the following numbers are divisible by 2,5,10?
1. 148
2. 5295
3. 2540
4. 34678
5. 7356
Solution:
1. 148
148 is divisible by 2 because in the unit digit 8 is the even number.
148 is not divisible by 5 because in the unit digit there is no zero or five.
148 is not divisible by 10 because it doesn’t end with 0.
Therefore, 148 is only divisible by 2 but not divisible by 5 and 10.
2. 5295
5295 is not divisible by 2 because in the unit digit there is an odd number 5.
5295 is divisible by 5 because in the unit digit there is five.
5295 is not divisible by 10 because it doesn’t end with 0.
Therefore, 5295 is divisible by 5 but not divisible by 2 and 10.
3. 2540
2540 is divisible by 2 because in the unit digit there is zero.
2540  is divisible by 5 because in the unit digit there is zero.
2540  is divisible by 10 because it ends with 0.
Therefore, 2540 is divisible by all 2,5, and 10.
4. 34678
34678 is divisible by 2 because in the unit digit there is an even number 8.
34678  is not divisible by 5 because in the unit digit there is no zero or five.
34678  is not divisible by 10 because it doesn’t end with 0.
Therefore, 34678 is divisible by 2 but not divisible by 5, and 10.
5. 7356
7356 is divisible by 2 because in the unit digit there is an even number 6.
7356  is not divisible by 5 because in the unit digit there is no zero or five.
7356  is not divisible by 10 because it doesn’t end with 0.
Therefore, 7356 is divisible by 2 but not divisible by 5, and 10.

II. Check whether the numbers are divisible by 4,8
1. 2312
2. 4832
3. 3440
4. 71480
5. 57235
Solution:
1. 2312
2312 is divisible by 4 because the last two digits are divisible by 4.
2312 is divisible by 8 because the last three digits are divisible by 8.
Hence, 2312 is divisible by both 4 and 8.
2. 4832
4832 is divisible by 4 because the last two digits are divisible by 4.
4832 is divisible by 8 because the last three digits are divisible by 8.
Hence, 4832 is divisible by both 4 and 8.
3. 3440
3440 is divisible by 4 because the last two digits are divisible by 4.
3440 is divisible by 8 because the last three digits are divisible by 8.
Hence,3440 is divisible by both 4 and 8.
4. 71480
71480 is divisible by 4 because the last two digits are divisible by 4.
71480 is divisible by 8 because the last three digits are divisible by 8.
Hence,71480 is divisible by both 4 and 8.
5. 57235
57235 is not divisible by 4 because the last two digits are divisible by 4.
57235 is not divisible by 8 because the last three digits are divisible by 8.
Hence,57235 is not divisible by both 4 and 8.

III. In each of the following numbers without doing actual division, determine whether the first number is  divisible by the second number
1. 1408512; 6
2.  15364; 6
3. 16803214; 8
4.  812592; 8
5. 152714; 4
Solution:
1. 1408512; 6
A number is divisible by 6 if the number is divisible by both 2 and 3.
1408512 is divisible by 2 because in the units digit there is an even number 2.
1408512 is divisible by 3 because the sum of digits is 21 and it is divisible by 3.
1408512 is divisible by both 2 and 3.
Hence, 1408512 is divisible by 6.
2. 15364; 6
15364 is divisible by 2 because in the units digit there is an even number 4.
15364 is divisible by 3 because the sum of digits is 21 and it is divisible by 3.
15364 is divisible by both 2 and 3.
Hence, 15364 is divisible by 6.
3. 16803214; 8
16803214 is not divisible by 8 because the last three digits are not divisible by 8.
4. 812592; 8
812592 is divisible by 8 because the last three digits are divisible by 8.
5. 152714; 4
152714 is not divisible by 4 because the last two digits are not divisible by 4.

IV. Is 9 a factor of the following?
1. 593274
2. 3842316
3. 6145320
Solution:
1. 593274
Sum of digits=5+9+3+2+7+4=30
30 is not divisible by 9.
Hence, 593274 is not divisible by 9.
2. 3842316
sum of digits=3+8+4+2+3+1+6=27
27 is divisible by 9.
So 3842316 is divisible by 9.
3. 6145320
sum of digits=6+1+4+5+3+2+0=21
21 is not divisible by 9.
Hence, 6145320 is not divisible by 9.

V. Fill the smallest digit to make the number divisible by:
1. by 5: 2142__, 94153__
2. by 3 : 2__13, 56__15, __426
3. by 6 : __326, 7__32, 431__
4. by 4 : 5372__, 72__ __, 823__
Solution:
1. by 5: 2142__, 94153__
A number is divisible by 5 if the last digit of the number is 0 or 5.
Here we have to fill the smallest number. So place 0 in the two blanks.
2. by 3 : 2__13, 56__15, __426
A number is divisible by 3 if the sum of the numbers is divisible by 3.
2+1+3=6
6 is divisible by 3.So place 0.
5+6+1+5=17
17 is not divisible by 3. The least number we can fill is 1.
It becomes 18. It is divisible by 3.
4+2+6=12
It is divisible by 3. So fill 0.
So fill 0,1,0 in the blanks.
3. by 6 : __326, 7__32, 431__
A number is divisible by 6 if it is divided by both 2 and 3.
The last digit 6 is an even number. So it is divisible by 2.
The Sum of digits is 3+2+6=11
The least digit we can place is 1. So it is divisible by both 2 and 3.
Hence, fill the blank with 1.
The last digit 2 is an even number. So it is divisible by 2.
The Sum of digits is 7+3+2=12
The least digit we can place is 0. So it is divisible by both 2 and 3.
4+3+1=8
Here we have to fill the blank with the smallest even number.
So that it should be divisible by both 2 and 3.
Fill the blank with 4.
104
4.  by 4 : 5372__, 72__ __, 823__
Fill the first blank with 0 such that the last two digits are divisible by 4.
Fill the next two blanks with 00.
Fill the next blank with 2 such that the last two digits are divisible by 4.

VI. Choose the right answer
1. The number with unit digit 0, 2, 4, 6, or 8 is divisible by
a) 2
b) 3
c) 4
d) 6
2. The number with unit digit 0 or 5 is divisible by
a) 3
b) 5
c) 6
d) 7
3. The number with unit digit 0 is divisible by
a) 2
b) 3
c) 4
d) 10
4. Which of the following numbers is not divisible by 2?
a) 18
b) 19
c) 22
d) 28
5. Which of the following numbers is not divisible by 10?
a) 200
b) 232
c) 500
d)800
Solution:
1. a
2. b
3. d
4. b
5. b

VII. Check using divisibility rules and fill in the boxes using “Yes” or “No”.

SNO Numbers 2 3 4 5 6 9 10
1 200 Yes No Yes Yes No No Yes
2 545 No No No Yes No No No
3 748 Yes No Yes No No No No
4 923 No No No No No No No
5 332 Yes No Yes No No No No
6 823 No No No No No No No

VIII. 6 is a factor of 13326 and 7332. Is 6 a factor of 13326+7332 and 13326-7332?
Solution:
Given 6 is a factor of 13326 and 7332.
The Sum of 13326 and 7332 is 20658.
Difference of 13326 and 7332 is 5994.
We have to find whether 20658 and 5994 are divisible by 6.
According to the Divisibility Rule,
A  number is divisible by 6 if it is divided by 2 and 3.
In 20658, 8 is in the unit’s place. it is divisible by 2. So 20658 is divisible by 2.
Sum of digits=2+0+6+5+8=21
21 is divisible by 3. So 20658 is divisible by 3.
Hence 20658 is divisible by 6.
!n 5994, 4 is in the unit’s place. So 5994 is divisible by 2.
Sum of digits=5+9+9+4=27
It is divisible by 3. So 5994 is divisible by 3.
Hence 5994 is divisible by 6.

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