DIVISIBILITY RULES
Divisibility by ‘6’ :- A natural number is divisible by 6, if it is divisible by 2 and 3 .
eg:- 30702
unit place contains ‘2’ then it is divisible by 2
3 + 0 + 7 + 0 + 2 = 12 is divisible by 3 then 30702 is divisible by 3
The given number is divisible by ‘6’
Note : - 2139 is not divisible by 6
9 is an odd number it is not divisible 2 2139 is not divisibel by 2139
2 + 1 + 3 + 9 = 15 is divisible by ‘3’
2139 is not divisible by 6
Divisibility by 7 :- Double the last digit (digit in even place) and subtract it from the remaining original number and continue doing until only digit remains , if the result is 0 (or) 7, then the given number is divisible by 0 (or) 7
Example: Consider \(\frac{{5613}}{b}\frac{3}{a}\)
\(b - 2a = 5613 - 6 = 5607\)
\(\frac{{560}}{b}\frac{7}{a}\)
b - 2a = 560-14 = 546
\(\frac{{54}}{b}\frac{6}{a}\)
b - 2a = 54 - 12 = 42
\(\frac{4}{b}\frac{2}{a}\)
b - 2a = 4 - 4 = 0
56133 is divisible by ‘7’
Divisibility by 8: A natural number is divisible by ‘8’ if the number formed by last three digit of the given number is divisible 8 (or) last 3 digit in the given number should contain zeros.
eg:- 136976 is divisible by 8 because 976 is divisible by 8
136976 is also divisible by 8
2) 437000 = 437 1000
1000 is divisible by ‘8’
4,37,000 is divisible by ‘8’