Maths 2 Mark Question

A given number is divisible by 11, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either O or a number divisible by 11.
7531622
Sum of digit at odd places = 7 + 3 + 6 + 2 = 18
Sum of digit at even places = 5 + 1 + 2 = 8
Difference of the above sum = (18 - 8) = 10
Which is divisible by 11
7531622 is divisible by 11

For a number to be divisible by 9, the sum of the digits must also be divisible by 9.
6 + 4 + y + 3 = 13 + y
For this to be divisible by 9:
y = 5
The number will be 6453.

A given number is divisible by 11, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either O or a number divisible by 11. 6543207 Sum of digit at odd places = 6 + 4 + 2 + 7 = 19 Sum of digit at even places = 5 + 3 + 0 = 8 Difference of the above sum = (19 - 8) = 11, Which is not divisible by 116543207 is not divisible by 11

For testing the divisibility of us of a number by 7, we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.
693
Now,
69 - (2 × 3) = 63, which is divisible by 7.
693 is divisible by 7.

The number 471z8 is divisible by 9
The sum of its digits is also divisible by 9
471z8 = 4 + 7 + 1 + z + 8
⇒ 20 + z is divisible by 9
Value of z can be 7
The numbers will be 47178.

The given number 53y1 is divisible by 3
The sum of its digits is divisible by 3
I.e., 5 + 3 + y + 1 or 9 + y is divisible by 3
Value of y can be 0, 3, 6, 9
Then The numbers can be 5301, 5331, 5361,5391

number x806 is divisible by 9
The sum of its digits is also divisible by 3
or x + 8 + 0 + 6 or 14 + x is divisible by 3
Value of x can be 4
The numbers will be 4806.

The given number 7x3 is divisible by 3
The sum of its digits is divisible by 3
7 + x + 3 ⇒ 10 + x is divisible by 3
Value of x can be 2, 5, 8
The number can be 723, 753, 783

A number is divisible by 9 if the sum of the digits is divisible by 9.

Number	Sum of the digit	Divisible by 9?
524618	26	No
7345845	36	Yes
8987148	45	Yes

For testing the divisibility of us of a number by 7, we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.
88777
Now,
8877 - (7 × 2) = 8863, which is divisible by 7.
88777 is divisible by 7.

For testing the divisibility of us of a number by 7, we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.
65436
Now,
6543 - (6 × 2) = 6531, which is divisible by 7.
65436 is divisible by 7.

A given number is divisible by 11, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either O or a number divisible by 11.379654
Sum of digit at odd places = 7 + 6 + 4 = 17 Sum of digit at even places = 3 + 9 + 5 = 17 Difference of the above sum = 17 - 17 = 0,379654 is divisible by 11

A given number is divisible by 11, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either O or a number divisible by 11. 818532 Sum of digit at odd places = 1 + 5 + 2 = 8 Sum of digit at even places = 8 + 8 + 3 = 19 Difference of the above sum = (19 - 8) = 11, Which is divisible by 11818532 is divisible by 11

A given number is divisible by 11, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either O or a number divisible by 11.
444444
Sum of digit at odd places = 4 + 4 + 4 = 12
Sum of digit at even places = 4 + 4 + 4= 12
Difference of the above sum = 12 - 12 = 0,
444444 divisible by 11

For testing the divisibility of us of a number by 7, we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.
98175
Now,
9817 - (5 × 2) = 9807, which is divisible by 7.
98175 is divisible by 7.

For testing the divisibility of us of a number by 7, we proceed according to the Following steps:
step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.
54636
Now,
5463 - (6 × 2) = 5451, which is divisible by 7.
54636 is divisible by 7.

A given number is divisible by 11, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either O or a number divisible by 11.1057982
Sum of digit at odd places = 1 + 5 + 9 + 2 = 17 Sum of digit at even places = 0 + 7 + 8 = 15 Difference of the above sum = (17 - 15) = 2, Which is not divisible by 111057982 is not divisible by 11

For testing the divisibility of us of a number by 7, we proceed according to the Following steps: Step I: Double the unit digit of the given number. Step II: Substract the above number from the number formed by excluding the unit digit of the given number. Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.12873
Now, 1287 - (3 × 2) = 1281, which is divisible by 7. 12873 is divisible by 7.

A given number is divisible by 11, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either O or a number divisible by 11. 900163 Sum of digit at odd places = 0 + 1 + 3 = 4 Sum of digit at even places = 9 + 0 + 6 = 15 Difference of the above sum = (15 - 4) = 11, Which is divisible by 11900163 is divisible by 11

For testing the divisibility of us of a number by 7, we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.
3467
Now,
346 - (7 × 2) = 332, which is divisible by 7.
3467 is not divisible by 7.

For testing the divisibility of us of a number by 7, we proceed according to the Following steps: Step I: Double the unit digit of the given number. Step II: Substract the above number from the number formed by excluding the unit digit of the given number. Step III: IF the number so obtained is divisible by 7 then the given number is divisible is 7.7896
Now, 789 - (6 × 2) = 777, which is divisible by 7. 7896 is divisible by 7.

Consider numbers as 36, 44, 52, 60. as these numbers are divisible by 4 not by 8.
Let the number 39, sum of digits 3 + 9 = 12
Which is divisible by 3 not by 9.