A number is divisible by 12 if:

Question

Examoogle · Accepted Answer

The correct answer is Option B: It is divisible by $3$ and $4$. Use the property that if $n = a 	imes b$ and $a, b$ are coprime (i.e., their HCF is 1), then divisibility by $n$ requires divisibility by both $a$ and $b$ simultaneously.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the property that if $n = a 	imes b$ and $a, b$ are coprime (i.e., their HCF is 1), then divisibility by $n$ requires divisibility by both $a$ and $b$ simultaneously.

Formula Used: $$n = 	ext{lcm}(a, b) \implies 	ext{if } \gcd(a, b) = 1, 	ext{ then } n | N \iff a | N 	ext{ and } b | N$$

Given: A number needs to be checked for divisibility by 12.

Steps: Factorize the divisor: To check divisibility by 12, factorize 12 into two numbers such that their greatest common divisor (GCD) is 1.. Apply divisibility rule: If a number is divisible by two coprime factors, it must be divisible by their product.. Verify other options: Option A (2 and 6) is incorrect because $\gcd(2, 6) = 2 
eq 1$. Option C (2 and 4) is incorrect because $\gcd(2, 4) = 2 
eq 1$. Option D (6 and 8) is incorrect because $\gcd(6, 8) = 2 
eq 1$.

Answer: B is correct because a number is divisible by $12$ if and only if it is divisible by its coprime factors $3$ and $4$.

Exam Tip: This rule applies to all composite numbers; always factorize the divisor into coprime factors (e.g., for divisibility by 72, check 8 and 9).

Examoogle · Answer

Option A: It is divisible by $2$ and $6$

Examoogle · Answer

Option C: It is divisible by $2$ and $4$

Examoogle · Answer

Option D: It is divisible by $6$ and $8$

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)