The smallest number that satisfies both conditions is 11 (11 % 3 = 2 and 11 % 5 = 1).

The smallest number satisfying both conditions is 22.

The smallest number that satisfies both conditions is 8 (8 % 5 = 3 and 8 % 3 = 2).

22 leaves a remainder of 2 when divided by 5, but it is not possible for 22 to leave a remainder of 2.

The smallest number that satisfies both conditions is 14 (14 % 10 = 4 and 14 % 3 = 2).

If the number is 6k + 4, then 3(6k + 4) = 18k + 12, which leaves a remainder of 0 when divided by 6.

The smallest number that satisfies both conditions is 23 (23 % 9 = 5 and 23 % 5 = 3).

The new number is 3*(11k + 6) = 33k + 18, which gives a remainder of 7 when divided by 11.

The new number is (original number - 3) = (10k + 7 - 3) = 10k + 4, which gives a remainder of 4.

The new number is (original number - 3), which gives a remainder of (7 - 3) = 4.

If the number is of the form 6k + 4, when divided by 3, it gives a remainder of 1 (4 % 3 = 1).

The maximum number of students is the HCF of 36 and 48, which is 12.

The HCF of 48 and 60 is 12, which is the maximum number of students she can distribute to equally.

The HCF of 48 and 60 is 12. Therefore, the largest number of students is 12.

The number of factors for each is: 10 (4), 12 (6), 15 (4), 18 (6). Arranging them gives 10, 12, 15, 18.

A number is divisible by 10 if it ends in 0.

A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or divisible by 11.

A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

The author illustrates the concept of digital sum through real-world applications, making it relatable and understandable.

The author presents a structured argument by outlining both the benefits and challenges associated with digital sum, providing a balanced view.

The author supports the claim about the efficiency of digital sum by discussing its computational advantages in various applications.

The author supports the claims about digital sum by citing recent technological advancements that utilize this concept.

A number is divisible by 15 if it is divisible by both 3 and 5. 70 is not divisible by 3.

A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 100 (1 + 0 + 0 = 1) is not divisible by 3.

'110' in base-2 = 1*2^2 + 1*2^1 + 0*2^0 = 4 + 2 + 0 = 6.

'1010' in binary is 1*8 + 0*4 + 1*2 + 0*1 = 10.

'1010' in binary is 10 in decimal, which is represented as 'A' in hexadecimal.

'A' represents 10, so 'B' represents 11 in decimal.

'A' = 10 in decimal, '5' = 5 in decimal. Their sum is 10 + 5 = 15.

In base-7, 'A' = 5*7^1 + 0*7^0 = 35 + 0 = 50 in decimal.