Which number is fully divided by 45?

Appeared in: SGPGI Nursing Officer-2022

Explanation

To be divisible by 45, a number must be divisible by its co-prime factors, which are 5 and 9.
The divisibility rule for 5 states that the number must end in a 0 or 5. The number 14625 ends in 5, so it is divisible by 5.
The divisibility rule for 9 states that the sum of the digits must be a multiple of 9.
For 14625, the sum of the digits is 1 + 4 + 6 + 2 + 5 = 18.
Since 18 is a multiple of 9 (18 ÷ 9 = 2), the number 14625 is also divisible by 9.
Because 14625 is divisible by both 5 and 9, it is fully divisible by 45.

Option B: The sum of its digits (1 + 2 + 9 + 9 + 5 = 26) is not divisible by 9.
Option C: This number is not divisible by 5 because its last digit is 6. It is also not divisible by 9 as the sum of its digits (1 + 6 + 2 + 4 + 6 = 19) is not a multiple of 9.
Option D: The sum of its digits (1 + 5 + 6 + 5 + 5 = 22) is not divisible by 9.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Divisibility rules in mathematics as background academic context rather than a clinical decision trigger.
Basic arithmetic skills, including understanding divisibility, are crucial for nurses to ensure patient safety through accurate medication dosage calculations.
Nurses frequently perform quick mental calculations for IV drip rates, converting units (e.g., mg to mcg), and managing supplies. Strong numeracy skills reduce the risk of errors.
What if a nurse needs to administer a total of 225 mg of a drug that comes in 45 mg tablets? Knowing that 225 is divisible by 45 (ends in 5, and 2+2+5=9) allows the nurse to quickly confirm that exactly 5 tablets are needed, preventing a medication error.

How to Approach the Question

First, identify the number the options must be divisible by, which is 45.
Break down 45 into its prime factors. The easiest co-prime factors to work with are 5 and 9 (5 × 9 = 45).
Recall the divisibility rule for 5: the number must end in 0 or 5. Use this rule to quickly eliminate any options that do not meet this criterion.
Recall the divisibility rule for 9: the sum of the number's digits must be divisible by 9.
Apply the rule for 9 to the remaining options.
The single option that satisfies both the rule for 5 and the rule for 9 is the correct answer.

Concept Tested & Keywords

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