Difficulty: Easy
Correct Answer: 34
Explanation:
Introduction:
In this aptitude question, you are asked to relate the product of two numbers with their least common multiple (LCM) in order to find their highest common factor (HCF). This is a standard number system concept that frequently appears in competitive exams and placement tests.
Given Data / Assumptions:
Concept / Approach:
The key concept used here is the fundamental relationship between HCF, LCM and the product of two numbers. For any two positive integers a and b, we use:
a * b = HCF(a, b) * LCM(a, b)This allows us to compute HCF if we know the product and the LCM.
Step-by-Step Solution:
Step 1: Write the relationship.a * b = HCF * LCMStep 2: Substitute the known values.3026 = HCF * 89Step 3: Solve for HCF by dividing the product by the LCM.HCF = 3026 / 89Step 4: Perform the division.89 * 34 = 3026, so HCF = 34
Verification / Alternative check:
We can also think of the two numbers as 89 * k and 34 * m with suitable integers k and m such that their product equals 3026. Since 3026 / 89 is exactly 34, it is reasonable that 34 is the common factor that fits the relation. The fact that the division is exact confirms the correctness.
Why Other Options Are Wrong:
33: If HCF were 33, then HCF * LCM = 33 * 89 = 2937, which is not equal to 3026.
35: 35 * 89 = 3115, again not matching the given product 3026.
29: 29 * 89 = 2581, also not equal to 3026.
38: 38 * 89 = 3382, which is greater than 3026 and incorrect.
Common Pitfalls:
Many students confuse the relationship between HCF, LCM and the product, or try to factorize the numbers directly, which is unnecessary here. Another common mistake is to think that HCF is simply a divisor of the LCM, which may not always help without using the proper formula.
Final Answer:
The highest common factor (HCF) of the two numbers is 34.
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