Question:
If 3 and 14 are factors of a number, which of the following can possibly be true? Indicate all possible answers.
If 3 and 14 are factors of a number, which of the following can possibly be true? Indicate all possible answers.
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If a number is divisible by two numbers, check divisibility using their LCM. This avoids missing extra factors.
Updated On: Sep 30, 2025
- Number is divisible by 6
- Number is always divisible by 2
- Number is divisible by 22
- Number is divisible by 3 \& 14 only
- Number is always a factor of 5
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The Correct Option is A
Solution and Explanation
Step 1: Apply LCM rule.
If a number is divisible by 3 and 14, then it must be divisible by LCM(3,14). \[ LCM(3,14) = 42 \] So any valid number is a multiple of 42.
Step 2: Check each option.
- (A) Divisible by 6: Since 42 is divisible by 6, the number must be divisible by 6.
- (B) Always divisible by 2: Since 42 is even, multiples of 42 are always even.
- (C) Divisible by 22: Not necessary (42 not divisible by 22).
- (D) Divisible by 3 \& 14 only: Wrong, because multiples of 42 will also be divisible by other numbers like 7, 21 etc.
- (E) Factor of 5: No such requirement.
Thus correct options are (A) and (B).
Final Answer: \[ \boxed{A, B} \]
If a number is divisible by 3 and 14, then it must be divisible by LCM(3,14). \[ LCM(3,14) = 42 \] So any valid number is a multiple of 42.
Step 2: Check each option.
- (A) Divisible by 6: Since 42 is divisible by 6, the number must be divisible by 6.
- (B) Always divisible by 2: Since 42 is even, multiples of 42 are always even.
- (C) Divisible by 22: Not necessary (42 not divisible by 22).
- (D) Divisible by 3 \& 14 only: Wrong, because multiples of 42 will also be divisible by other numbers like 7, 21 etc.
- (E) Factor of 5: No such requirement.
Thus correct options are (A) and (B).
Final Answer: \[ \boxed{A, B} \]
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