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Assertion and Reason Question
15. Assertion (A)-The factors of 8 are 1, 2, 4, 8.
Reason (R)- every factor of a number is an exact divisor of that number.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is not the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Verified Answer :

GinnyAnswer

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.

- \(\(1\)\) is a factor of \(\(8\)\) because \(\(8 ÷ 1 = 8\)\) (no remainder).
- \(\(2\)\) is a factor of \(\(8\)\) because \(\(8 ÷ 2 = 4\)\) (no remainder).
- \(\(4\)\) is a factor of \(\(8\)\) because \(\(8 ÷ 4 = 2\)\) (no remainder).
- \(\(8\)\) is a factor of \(\(8\)\) because \(\(8 ÷ 8 = 1\)\) (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

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