Q.1 Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3:
(a) _ 6724
(b) 4765_ 2
Q.2 Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:
(a) 92_389
(b) 8_9484
Q.3 Write all the numbers less than 100 which are common multiples of 3 and 4.
Q.4 A number is divisible by 12. By what other numbers will that number be divisible?
Q.5 A number is divisible by both 5 and 12. By which other number will that number be always divisible.
These are my hard 5 question please answers the questions.
Thank you.
Answers
Answer:
Step-by-step explanation:
a) 2
b) 3
a)8
b) 6
Q3 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88,92,96.
Q4 By what other numbers will that number be divisible? Given that a number is divisible by 12. Factors of 12 are 1, 2,3,4,6, and 12. So the number 12 will be divisible by 1,2,3,4,6 and 12.
Q 5 By which other number will that number be always divisible? Solution: The number is divisible by 5 and 12. Since 5 and 12 are co-prime numbers so the number must be divisible by the product 5 × 12 = 60. So, the given number will always be divisible by 60.
Answer:
Step-by-step explanation:
1)A number is divisible by 3 if its sum of all digits is divisible by 3
(a) ___6724
6+7+2+4= 19
if we add 2 then the digit is divisible by 3 ( 19+2=21)
2 is the smallest digit
26724 = 2 + 6 + 7 + 2 + 4 = 21
if we add 8 then the digit is divisible by 3 ( 19+8=27)
8 is the largest digit
26724 = 8+ 6 + 7 + 2 + 4 = 36
b) 4765 ___2
4+7+6+5+2=24
if we add 0 then the digit is divisible by 3 ( 24+0=24)
0 is the smallest digit
4765 ___2 = 4+ 7+6+5+0+2= 24
if we add 9 then the digit is divisible by 3 ( 24+9=33)
9 is the largest digit
4765 ___2 =4+ 7+6+5+9+2= 33
2)a)For a no. to be divisible by 11, this difference should be zero or a multiple of 11.
sum of digits of odd places - sum of digits of even places=0 or multiple of 11
the answer should be 8
b)Let a be placed in the blank.
Sum of the digits at odd places = 4 + 4 + a = 8+a
Sum of the digit at even places = 8 + 9 + 8 = 25
Difference = 25 - (8-a) = 17 - a
For a no. to be divisible by 11, this difference should be zero or a multiple of 11.
If 17 - a = 0
then, a = 17
This is not possible.
A multiple of 11 has to be taken..taking 11 we obtain
17 - a = 11
a = 6
Therefore the required digit is 6..
3)Multiple of 3 = 12,24,36, 39,48,60,72 and 96,
Multiple of 4 = 12, 24,36,48,60,72,84 and 96
4)Given that a number is divisible by 12. Factors of 12 are 1, 2,3,4,6, and 12. So the number 12 will be divisible by 1,2,3,4,6 and 12.
5)The number is divisible by 5 and 12. Since 5 and 12 are co-prime numbers so the number must be divisible by the product 5 × 12 = 60. So, the given number will always be divisible by 60.
------------------------------------------------------------------------------------------------------
Hope this will help you