Number System Shortcut: Quiz!

All the numbers given in the list are divisible by 2 except for the number 5. This is because a number is divisible by 2 if it can be divided evenly by 2 without leaving a remainder. In the case of 5, it cannot be divided evenly by 2 as 5 divided by 2 equals 2 with a remainder of 1. Therefore, 5 is not divisible by 2.

The number 3 is not among the even numbers because it is an odd number. Even numbers are divisible by 2, while odd numbers are not. In this case, 2, 4, and 6 are all divisible by 2 and therefore even, but 3 is not.

The operation known as product in the number system is multiplication. This operation involves combining two or more numbers to find the total value of their repeated addition. It is represented by the symbol "×" or "*", and is used to calculate the total quantity or value when multiple groups of the same size are combined.

The number 14 is divisible by only 2 and 7. It is divisible by 2 because it is an even number, and it is divisible by 7 because there is no remainder when 14 is divided by 7. Therefore, 14 is the only number in the given options that satisfies the condition of being divisible by only 2 and 7.

The term given to a number raised to the power of two is "square".

Numbers that are divisible by 2 are called even numbers. This is because even numbers can be divided into two equal parts without any remainder. For example, 4, 8, and 12 are all divisible by 2 and therefore considered even numbers.

Prime numbers are a special type of numbers that are only divisible by 1 and itself. They cannot be divided evenly by any other numbers. Decimal numbers, even numbers, and odd numbers do not have this property. Therefore, the correct answer is prime numbers.

Deduction is not an operation relating to number systems. Division, addition, and subtraction are all mathematical operations that are commonly used in number systems. Deduction, on the other hand, is a logical reasoning process used to reach a conclusion based on given information. It is not specifically related to number systems.

The formula for the sum of n even numbers is n(n+1). This can be derived by considering that the sum of the first n even numbers is equal to the sum of the first n natural numbers multiplied by 2. The sum of the first n natural numbers is given by the formula n(n+1)/2, and when multiplied by 2, it becomes n(n+1).

The formula for the sum of the first n odd numbers is n². This can be derived by observing that the first odd number is 1, the second odd number is 3, the third odd number is 5, and so on. It can be noticed that each odd number can be represented as 2k-1, where k is the position of the odd number. By summing up the first n odd numbers using this representation, it can be simplified to n².