1. Divisibility 4,8 and 11

2. Divisibility 4 rule
If the digits in the ones place & tens place together are divisible by 4, then number is divisible by 4.
For Example 484
HUNDREDS
TENS
ONES 4 8 4
The digits in the ones place & tens place together is 84
84 is divisible by 4
∴ 484 is divisible by 4.

3. Divisibility 4 rule 490 345 612 781 932 ∴ 490 is not divisible by 4
The digits in the ones place & tens place together = 90.
90 is not divisible by 4.
∴ 490 is not divisible by 4
345
The digits in the ones place & tens place together = 45.
45 is not divisible by 4.
∴ 345 is not divisible by 4
612
The digits in the ones place & tens place together = 12.
12 is divisible by 4.
∴ 612 is divisible by 4
781
The digits in the ones place & tens place together = 81.
81 is not divisible by 4.
∴ 781 is not divisible by 4
932
The digits in the ones place & tens place together = 32.
32 is divisible by 4.
∴ 932 is divisible by 4

4. Divisibility 8 rule
In a number if the digits in the ones place & tens & hundreds place together is divisible by 8 , then number is divisible by 8.
For Example 9160
THOUSANDS
HUNDREDS
TENS
ONES 9 1 6
The digits in the ones place & tens & hundreds place together is 160
160 is divisible by 8
∴ 9160 is divisible by 8.

5. Divisibility 8 rule
1335
The digits in the ones place & tens & hundreds place together = 335.
335 is not divisible by 8.
∴ 1335 is not divisible by 8
9032
The digits in the ones place & tens & hundreds place together = 32.
32 is divisible by 8.
∴ 9032 is divisible by 8
6126
The digits in the ones place & tens & hundreds place together = 126.
126 is not divisible by 8.
∴ 6126 is not divisible by 8
2379
The digits in the ones place & tens & hundreds place together = 379.
379 is not divisible by 8.
∴ 2379 is not divisible by 8
5320
The digits in the ones place & tens & hundreds place together = 320.
320 is divisible by 8.
∴ 5320 is divisible by 8

6. Divisibility Rule for 11 1 5 7 3 Digits 1 2 3 4
If the difference between sum of digits in even places and sum of digits in odd digits is 0 or divisible by 11.
For example:-Take the number 1573
Digits 1 2 3 4 1 5 7 3
The digits in odd place are 1 and 7. Sum of digits in odd place =1+7=8.
The digits in even places are 5 and 3. Sum of digits in even places =5+3=8.
Difference between sum of even digits and odd digits 8 – 8 =0
Hence 1573 is divisible by 11

7. Divisibility 11 rule
2478
The sum of odd digits is 2+7=9.
The sum of even digits is 4+8=12.
The difference is 12-9=3 .
3 is not divisible by 11.
∴ 2478 is not divisible by 11
5612
The sum of odd digits is 5+1=6.
The sum of even digits is 6+2=8.
The difference is 8-6=2.
2 is not divisible by 11.
∴ 5612 is not divisible by 11
1364
The sum of odd digits is 1+6=7.
The sum of even digits is 3+4=7.
The difference is 7-7=0.
∴ 1364 is divisible by 11
7962
The sum of odd digits is 7+6=13.
The sum of even digits is 9+2=11.
The difference is 13-11=2.
2 is not divisible by 11.
∴ 7962 is not divisible by 11
3729
The sum of odd digits is 3+2=5.
The sum of even digits is 7+9=16.
The difference is 16-5=11.
11 is divisible by 11.
∴ 3729 is divisible by 11
3670
The sum of odd digits is 3+7=10.
The sum of even digits is 6+0=6.
The difference is 10-6=4.
4 is not divisible by 11
∴ 3670 is not divisible by 11

8. Try these From the given number below, list the numbers divisible by 4
2532 , 4513 , 3560 , , 5240
From the given number below, list the numbers divisible by 8
1040 , 3210, 2120 , 4405 , 5240
From the given numbers below, list the numbers divisible by 11
1364 , 5113 , 987, 913 , 3729

9. Revision1
From the given numbers below, list the numbers divisible by 3
351 , 125 , 243 , 502 , 603
From the given number below, list the numbers divisible by 6
2010 , 5212, 4023 , 3145 , 1452
From the given number below, list the numbers divisible by 9
3512 , 1747 , 2547 , 5013, 4878

10. Revision2
From the given numbers below, list the numbers divisible by 2
245 , 178 , 356 , 458 , 564
From the given number below, list the numbers divisible by 5
2138 , 1375, 5031 , , 4560
From the given number below, list the numbers divisible by 10
3150 , 2165 , 5161 , 1213 , 4230