check the divisibility condition of the number by3, 6and11
Answers
for 6= no. should be divisible by both2 and 3
for 11= sum of alternate no. sgould add upto 0
Divisibility rules are certain rules which help us to determine the actual divisor of a number just by considering the digits of the number.
Ф Divisibility by 3:
Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3 i.e., it is a multiple of 3
Consider a number, 308.To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3 then the original number is also divisible by 3. Here, since 11 is not divisible by 3, 308 is also not divisible by 3.
Similarly, 516 is divisible by 3 completely as the sum of its digits i.e. 5+1+6=12, is a multiple of 3.
Ф Divisibility by 6:
Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.
Consider 630, the number is divisible by 2 as the last digit is 0.
The sum of digits is 6+3+0 = 9, which is also divisible by 3.Hence 630 is divisible by 6.
Ф Divisibility by 11:
If the difference of the sum of alternative digits of a number is divisible by 11 then that number is divisible by 11 completely.
In order to check whether a number like 2143 is divisible by 11 following is the procedure.
⇒ Group the alternative digits i.e. digits which are in odd places together and digits in even places together. Here 24 and 13 are two groups.
⇒ Take the sum of the digits of each group i.e. 2+4=6 and 1+3= 4
⇒ Now find the difference of the sums; 6-4=2
⇒ If the difference is divisible by 11, then the original number is also divisible by 11. Here 2 is the difference which is not divisible by 11.
⇒ Therefore, 2143 is not divisible by 11.
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