All questions of Integers for Year 8 Exam

Understanding Common Factors
When discussing factors in mathematics, it’s important to define what a common factor is. A common factor is a number that can exactly divide two or more numbers without leaving a remainder.
Definition of a Common Factor
- A common factor is a divisor of two or more numbers.
- For example, if we take the numbers 12 and 18, the common factors are 1, 2, 3, and 6.
Importance of Common Factors
- Common factors are significant in various mathematical operations, such as simplifying fractions and finding greatest common divisors (GCD).
- They help in determining the relationship between numbers and play a key role in number theory.
Why 'Common' is the Correct Answer
- The term "common" signifies that the factor is shared among the numbers being considered.
- In the context of the question, since the number divides exactly into two other numbers, it is indeed a common factor of those two numbers.
Examples of Common Factors
- For the numbers 15 and 25, the common factors are 1 and 5.
- This indicates that both numbers are divisible by 5, making it a common factor.
In conclusion, when a number divides exactly into two other numbers, it is identified as a common factor, making option 'C' the correct answer. Understanding this concept is essential for further studies in mathematics.

One negative and one positive number equals a negative result

Understanding Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Let's analyze the options provided to identify which one is prime.
Options Analysis
- Option A: 16
- Divisors: 1, 2, 4, 8, 16
- Since it has divisors other than 1 and itself, 16 is not a prime number.
- Option B: 23
- Divisors: 1, 23
- It has no divisors other than 1 and 23, so 23 is a prime number.
- Option C: 42
- Divisors: 1, 2, 3, 6, 7, 14, 21, 42
- With multiple divisors, 42 is not a prime number.
- Option D: 51
- Divisors: 1, 3, 17, 51
- Since it has divisors other than 1 and itself, 51 is not a prime number.
Conclusion
Among the given options, the only prime number is 23. It stands out because it can only be divided evenly by 1 and itself, confirming its status as a prime number.
Thus, the correct answer is option B: 23.

In all the incorrect answers there is a number that will not divide into 80 and give a whole number as the result

Understanding Factors
Factors are numbers that can be multiplied together to get another number. To determine if one number is a factor of another, we check if the second number can be evenly divided by the first number.
Calculating Factors of 21
To see if 4 is a factor of 21, we divide 21 by 4:
- 21 ÷ 4 = 5.25
Since 21 does not divide evenly by 4 (the result is not a whole number), we can conclude that 4 is not a factor of 21.
Definition of a Factor
A factor of a number is defined as:
- A whole number that can divide the original number without leaving a remainder.
Since dividing 21 by 4 results in a decimal (5.25), it indicates that there is a remainder. Therefore, 4 cannot be considered a factor of 21.
Conclusion
- The correct answer is option 'B': No, 4 is not a factor of 21.
Understanding factors is essential in mathematics, especially in topics such as fractions, ratios, and number theory. By recognizing that 4 does not evenly divide 21, we can confidently affirm its status as a non-factor of the number.

The square root of 100 could be either 10 or -10 and we have no way of knowing which square root the question requires!

The calculation in brackets is a negative ÷ a negative so the answer will be a positive. We then divide this positive by a negative so the answer will be a negative