Maths Solve The Following Question.1MARKS

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,591282 - 5 + 9 + 1 + 2 + 8 = 27, is divisble by 3

We know that a number is divisible by 10 if its unit digit is 0.
90
The number 90 has '0' at its unit's place so, it is divisible by 10.

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.
22222
Sum of digit at odd places = 2 + 2 + 2 = 6
Sum of digit at even places = 2 + 2 = 4
Difference of the above sum = 6 - 4 = 2
which is not divisible by 11
22222 is not divisible by 11

We know that a number is divisible by 10 if its unit digit is 0.
205
The number 205 has '5' at its unit's place so, it is not divisible by 10.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
66664, is divisible by 8 as last three digits 664 is divisible by 8.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
32022
3 + 2 + 0 + 2 + 2 = 9, is divisible by 9.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
39392, is not divisible by 4 as last two digits 92 is not divisible by 4.

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
95
The number 95 has '5' at its unit's place so, it is divisible by 5.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
7350162, is not divisible by 8 as last three digits 162 is not divisible by 8.

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
285
The number 285 has '5' at its unit's place so, it is divisible by 2.

4. 3.

Solution:
If a number is divisible by 3, the sum of the digits is also divisible by 3.
4 + x + y + 7 = 11 + (x + y)
For the sum to be divisible by 3:
11 + (x + y) = 12
⇒ (x + y) = 1

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
89361
8 + 9 + 3 + 6 + 1 = 27, is divisible by 9.

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
98765
The number 98765 has '5' at its unit's place so, it is divisible by 5.

A given number is dovisible by 8 only when the number formed by its last three digits is divisible by 8.6132, is not divisible by 8 as last three digits 132 is not divisible by 8.

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
66669
The number 66669 has '9' at its unit's place so, it is divisible by 2.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,903164 - 9 + 0 + 3 + 1 + 6 + 4 = 23, is not divisble by 3

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
46821
The number 46821 has '1' at its unit's place so, it is divisible by 2.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
99918, is not divisible by 4 as last two digits 18 is not divisible by 4.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3.
Therefore,
83 - 8 + 3 = 11, is not divisble by 3

Let the two numbers of the two-digit number be 'a' and 'b'.
a + b = 6a + b = 6 ....(1)
The number can be written as (10a + b)(10a + b).
After interchanging the digits, the number becomes (10b + a).
(10a + b) + 18 = (10b + a)
9a - 9b = -18
a - b = -2a - b = -2 ....(2)
2a = 4
⇒ a = 2
Using a = 2a = 2 in equation(1)
b = 6 - a = 6 - 2 = 4
Therefore, the original number is 24.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
66888
6 + 6 + 8 + 8 + 8 = 36, is divisible by 9.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
265472, is divisible by 8 as last three digits 472 is not divisible by 8.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
3928, is divisible by 4 as last two digits 28 is divisible by 4.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
56794, is not divisible by 4 as last two digits 94 is not divisible by 4.

2. 0

Solution:

If a number is exactly divisible by 3, the sum of its digits is also divisible by 3.

7 + x + 8 = 15 + x

15 + x can be divisible by 3 even if x is equal to 0.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
44444, is not divisible by 8 as last three digits 444 is not divisible by 8.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
77736, is divisible by 4 as last two digits 18 is divisible by 4.

The three whole numbers are 1, 2 and 3.
1 + 2 + 3 = 6 = 1 × 2 × 3

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
42658
The number 42658 has '8' at its unit's place so, it is divisible by 5.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,20345 - 2 + 0 + 3 + 4 + 5 = 14, is not divisble by 3

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
66666, is not divisible by 4 as last two digits 66 is not divisible by 4.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
327
3 + 2 + 7 = 12, is not divisible by 9.

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
35790
The number 35790 has '0' at its unit's place so, it is divisible by 5.

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
13576
The number 13576 has '6' at its unit's place so, it is divisible by 2.

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
79532
The number 79532 has '2' at its unit's place so, it is divisible by 2.

We know that a number is divisible by 10 if its unit digit is 0.
1174
The number 1174 has '4' at its unit's place so, it is not divisible by 10.

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
570
The number 570 has '0' at its unit's place so, it is divisible by 2.

We know that a number is divisible by 10 if its unit digit is 0.
60005
The number 60005 has '5' at its unit's place so, it is not divisible by 10.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,378 - 3 + 7 + 8 = 18, is divisble by 3

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
2398
The number 2398 has '8' at its unit's place so, it is divisible by 2.

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
94
The number 94 has '4' at its unit's place so, it is divisible by 2.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
59312, is divisible by 8 as last three digits 312 is divisible by 8.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
86102, is not divisible by 4 as last two digits 02 is not divisible by 4.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4. Therefore,618, is not divisible by 4 as last two digits 18 is not divisible by 4.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,100002 - 1 + 0 + 0 + 0 + 0 + 2 = 3, is not divisble by 3

We know that a number is divisible by 2 only when its unit digit is 0, 2, 4, 6 or 8.
84663
The number 84663 has '3' at its unit's place so, it is divisible by 2.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,474 - 4 + 7 + 4 = 15, is divisble by 3

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4.
Therefore,
50176, is not divisible by 4 as last two digits 76 is not divisible by 4.

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
2735
The number 2735 has '5' at its unit's place so, it is divisible by 5.

We know that a number is divisible by 4, only when the number formed by its last two digits is divisible by 4. Therefore,134, is not divisible by 4 as last two digits 34 is not divisible by 4.

We know that a number is divisible by 10 if its unit digit is 0.
57930
The number 57930 has '0' at its unit's place so, it is not divisible by 10.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,1693 - 1 + 6 + 9 + 3 = 19, divisble by 3

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
77990
The number 77990 has '0' at its unit's place so, it is divisible by 5.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
7524
7 + 5 + 2 + 4 = 18, is divisible by 9.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
33333
3 + 3 + 3 + 3 + 3 = 15, is not divisible by 9.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
14799
1 + 4 + 7 + 9 + 9 + 9 = 30, is not divisible by 9.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9. Therefore,64302
6 + 4 + 3 + 0 + 2 = 15, is not divisible by 9.

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
1056
The number 1056 has '6' at its unit's place so, it is divisible by 5.

We know that a number is divisible by 9, if the sum of its digitals is divisible by 9.
Therefore,
30006
3 + 0 + 0 + 0 + 6 = 9, is divisible by 9.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
7304, is divisible by 8 as last three digits 304 is not divisible by 8.

We know that a number is divisible by 3 if the sum of its digits is divisible by 3 if the sum of its digits is divisble by 3. Therefore,67035 - 6 + 7 + 0 + 3 + 5 = 21, divisble by 3

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
55053
The number 55053 has '3' at its unit's place so, it is divisible by 5.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
154360, is divisible by 8 as last three digits 360 is not divisible by 8.

A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.Therefore,
998818, is not divisible by 8 as last three digits 818 is not divisible by 8.

We know that a number is divisible by 5 its unit digit is 0 or 5.
Therefore,
470
The number 470 has '0' at its unit's place so, it is divisible by 5.