write down the rules for test of divisibility of numbers for the following with example divisibility by 2,3,4,5,6,8,9,10 and 11
Answers
Divisibility of 2 : The last digit of the number should be divisible by 2 (i.e when the last digit is divided by 2 answer should be 0).
Ex : 1758, last digit is 8 and 8 is divisible by 2. Therefore 1758 is divisible by 2.
Divisibility of 3 : If the sum of digits of the number is divisible by 3, then the number is divisible by 3.
Ex : 15921, sum of digits = 1 + 5 + 9 + 2 + 1 = 18 & 18 is divisible by 3. Therefore 15921 is divisible by 3.
Divisibility of 4 : If the last two digits of the number are divisible by 4, then the number is divisible by 4.
Ex : 7520, last two digits are 20 & 20 is divisible by 4. Therefore 7520 is divisible by 4.
Divisibility of 5: If the number ends with 0 or 5, then the number is divisible by 5.
Ex : 3475, It ends with 5 so it is divisible by 5.
Divisibility of 6 : If the number is divisible by both 2 & 3, then it is divisible by 6.
Ex : 15912, Sum of digits = 18 so it is divisible by 3 and last digit is divisible by 2. Therefore the number is divisible by 6.
Divisibility of 8 : If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
Ex: Take number 24344. Consider the last three digits i.e. 344. As 344 is divisible by 8, the original number 24344 is also divisible by 8.
Divisibility of 9 : If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.
Ex: Consider 783, as the sum of its digits 7+8+3 is 18, which is divisible by 9, hence 783 is divisible by 9.
Divisibility of 10 : If the number ends with 0, then it is divisible by 10.
Ex : 9340, last digit is 0. Therefore it is divisible by 10.
Divisibility of 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.
If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number.
Example: 3784
Number of digits = 4
Now, 78 + 3 – 4 = 77 = 7 × 11
Thus, 3784 is divisible by 11.
If the number of digits of a number is odd, then subtract the first and the last digits from the rest of the number.
Example: 82907
Number of digits = 5
Now, 290 – 8 – 7 = 275 × 11
Thus, 82907 is divisible by 11.
Form the groups of two digits from the right end digit to the left end of the number and add the resultant groups. If the sum is a multiple of 11, then the number is divisible by 11.
Example: 3774 := 37 + 74 = 111 := 1 + 11 = 12
3774 is not divisible by 11.
253 := 2 + 53 = 55 = 5 × 11
253 is divisible by 11.
Subtract the last digit of the number from the rest of the number. If the resultant value is a multiple of 11, then the original number will be divisible by 11.
Example: 9647
9647 := 964 – 7 = 957
957 := 95 – 7 = 88 = 8 × 11
Thus, 9647 is divisible by 11