250 divided by 7 gives a quotient of 35 and a remainder of 5.

256 divided by 7 gives a quotient of 36 and a remainder of 4.

The sum of the digits of 987654 is 39, which is divisible by 9, hence the remainder is 0.

Adding 1011 and 1101 in binary results in 11110.

The passage highlights that digital sum plays a crucial role in enhancing the accuracy of data interpretation.

In binary, '101' + '110' = '1011'.

1000 divided by 6 gives a remainder of 4.

Since 6 mod 3 = 0, the remainder when the number is divided by 3 is also 0.

The hexadecimal system is most efficient for representing large binary numbers due to its compactness.

The binary system is primarily used in digital electronics due to its two-state nature.

In a positional numeral system, the position of a digit determines its value, such as in decimal or binary systems.

The author presents digital sum in an enthusiastic manner, providing informative insights into its significance.

The conclusion emphasizes that digital sum is fundamental and has numerous applications across various domains.

8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.

The hexadecimal system is a base-16 system that includes the digits 0-9 and letters A-F.

For a number to be divisible by 11, the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11.

To check for divisibility by 7, you can double the last digit and subtract it from the rest of the number.

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

Modular arithmetic is commutative for addition and multiplication, hence non-commutativity is not a property.

'22' cannot represent 10 in any base since it would require base 3 or higher.

A factor is defined as a number that divides another number without leaving a remainder.

The decimal number 15 is represented as '1111' in binary.

The GCD of 48 and 180 is 12, as it is the largest number that divides both without a remainder.

12 is the smallest number that is a multiple of both 4 and 6.

The LCM of 8 and 12 is 24, which is a multiple of both.

121 is divisible by 11, as 121 = 11 x 11.

A number is divisible by 8 if the last three digits form a number that is divisible by 8. 64 is divisible by 8.

55 is not divisible by 12, as it does not meet the criteria of being divisible by both 3 and 4.

A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 22 (2 + 2 = 4) is not divisible by 3.

The HCF of 15 and 28 is 1, making them coprime.