Exercise 6.3.4
5. 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 :
To get,A number is divisible by 3 if the sum of its digits is divisible by 3.
a.
b.4765
4765
6. Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11
A number is divisible by 11 if the alternating sum of its digits is divisible by 11
a.The digit is 92
b.The digit is 8
- To find the common factors of two numbers, we need to list the factors of each number and then identify the factors that they have in common.
- For 20 and 28 so factors of 20 is 1, 2,
, 5, 10, 20 and for 28 is 1, 2, 4, 7, , 28. - Common factors are:
, , . - And 15 and 25 so Factors of 15 is 1, 3,
, 15 and Factors of 25 is 1, 5, . - Common factors are :
,
- To find the common factors of multiple numbers, we list the factors of each number and identify the factors they have in common.
- For 4, 8 and 12 so Factors of 4 is 1, 2, 4 and Factors of 8: 1, 2, 4, 8 and Factors of 12: 1, 2, 3, 4, 6, 12.
- Common factors are:
, , . - For 5, 15 and 25 so factors of 5 is 1, 5 and Factors of 15: 1, 3, 5, 15 and Factors of 25: 1, 5, 25
- Common factors are:
, .
- Find first three common multiples of :
a. 6 and 8 :
multiples of 6 : 6, 12,
mutltipes of 8 : 8, 16, 24,
The first three common multiples are:
b. 12 and 18 :
Multiples of 12: 12, 24,
Multiples of 18: 18, 36,
The first three common multiples are:
- 4.Let us take the LCM of 3 and 4 .
- Prime factorization of 3: 1x
. - Prime factorization of 4: 1x
x . - LCM Of 3 and 4 is 1x2x2x3=12.
- Now, the multiples of 12 are the common multiples of 3 and 4 which are less than are:12,
, , , 60, , 84, 96. - Thus, numbers less than 100 are 12, 24, 36, 48, 60, 72, 84, 96.
5 .Which of the following numbers are co-prime?
6. A number is divisible by both 5 and 12. By which other number will that number be always divisible?
We have to find another number by which the given number is always divisible.
The common factors of 5 and 12 only 1 therefore they are co-primes a number is divisible by two co-primes, then it is also divisible by their product.
so, 5x12=
Thus the number is always divisible by 60.
- A number is divisible by 12. By what other numbers will that number be divisible?
If a number is divisible by 12, it means it is a multiple of 12. To find the other numbers by which it will be divisible, we need to find the factors of 12.
The factors of 12 are 1,
Therefore, a number that is divisible by 12 will also be divisible by 1, 2, 3, 4, 6, and 12.