in 3409122 divisible by 11,12 and 13
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Divisibility Rule for 11
Divide the alternate digits in two different groups. Take the sum of alternate digits separately and find the difference of the two numbers. If the difference is 0 or is divisible 11, the number is divisible by 11.
Example: 86456293 is divided into two groups {8,4,6,9} and {6,5,2,3}. Sum of the groups is 27 and 16, whose difference is 11 and the it is divisible by 11, 86456293 is divisible by 11.
Divisibility Rule for 12
If the number is divisible by both 3 and 4, the number is divisible by 12. Divisibility rule of 3 is tat sum of digits is divisible by 3 and divisibility rule of 4 is that last two digits are divisible by 4.
Example: In 185176368 sum of all the digits is 45 and is divisible by 3 and also last two digits 68 are divisible by 4. As such the number 185176368 is divisible by 12.
Divisibility Rule for 13
Recall the divisibility rule of 7, this works for 13 too.
Starting from right mark off the digits in groups of threes (just as we do when we put commas in large numbers).
Now add up alternate group of numbers and find the difference between the two. If the difference is divisible by 13, entire number is divisible by 13.
For example 123448789113, these are grouped as 123, 448, 789 and 113
and 123+789=912 and 448+113=561.
As difference between 912−561=351
As 351 is divisible by 13, 123448789113 is divisible by 13