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

Since 18 = 2 × 9, being a multiple of 9 is necessary for a number to be a multiple of 18.

To check for divisibility by 7, you can double the last digit and subtract it from the rest of the number; if the result is divisible by 7, then the original number is also divisible by 7.

The passage mentions that a potential drawback of digital sum is that it may lead to oversimplification of data, which can be problematic.

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 a multiple of 11.

A number is divisible by 3 if the sum of its digits is divisible by 3.

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 0 or divisible by 11.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Prime numbers are defined as having exactly two distinct positive divisors: 1 and the number itself.

The first multiple of any number is indeed the number itself, while the other statements are false.

In base-4, valid digits are 0, 1, 2, and 3. Therefore, 123 is valid, while 234, 345, and 456 contain digits not allowed in base-4.

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

In base 8, 15 is represented as '17' (1*8 + 7).

√2 is an irrational number because it cannot be expressed as a fraction of two integers.

Multiples can be both odd and even; hence, they are not always odd.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. 7 is not among them.

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. 9 is not prime as it can be divided by 3.

An even number is not always a prime number; in fact, the only even prime number is 2.

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

In base-3, only digits 0, 1, and 2 are valid. '30' is invalid.

In base 4, the digits can only be 0, 1, 2, or 3. '24' is invalid.

The octal system only uses digits 0-7, so 8 is not a valid numeral.

In base 3, only digits 0, 1, and 2 are valid. '230' contains '3', which is invalid.

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

The passage does not mention enhanced data security as a benefit of digital sum.

The passage does not mention data compression techniques as an application of digital sum.

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

The binary representation of the decimal number 8 is 1000.

The decimal number 10 is represented as 1010 in binary.

Binary is the simplest (base-2), followed by Decimal (base-10), and then Hexadecimal (base-16), making the correct order Binary, Decimal, Hexadecimal.