Let's break down the assertion and the reason to evaluate them separately.
Assertion (A): The factors of 8 are 1, 2, 4, 8.
To determine if the assertion is true, we must verify if the listed factors are indeed the factors of 8. A factor of a number is defined as a number that divides the given number without leaving any remainder.
- [tex]\(1\)[/tex] is a factor of [tex]\(8\)[/tex] because [tex]\(8 ÷ 1 = 8\)[/tex] (no remainder).
- [tex]\(2\)[/tex] is a factor of [tex]\(8\)[/tex] because [tex]\(8 ÷ 2 = 4\)[/tex] (no remainder).
- [tex]\(4\)[/tex] is a factor of [tex]\(8\)[/tex] because [tex]\(8 ÷ 4 = 2\)[/tex] (no remainder).
- [tex]\(8\)[/tex] is a factor of [tex]\(8\)[/tex] because [tex]\(8 ÷ 8 = 1\)[/tex] (no remainder).
Therefore, the assertion that the factors of 8 are 1, 2, 4, and 8 is correct.
Reason (R): Every factor of a number is an exact divisor of that number.
A factor of a number is defined as a number that divides the given number completely, i.e., without leaving a remainder. Therefore, by definition, every factor of a number is indeed an exact divisor of that number.
Thus, the reason is correct.
Evaluation of both Assertion (A) and Reason (R):
- We have established that both Assertion (A) and Reason (R) are true.
- Furthermore, Reason (R) correctly explains why the list of numbers (1, 2, 4, 8) are factors of 8. It is because each of these numbers divides 8 exactly.
Therefore, the correct answer is:
a) Both A and R are true and R is the correct explanation of A
