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HCF & LCM
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NTPC Graduate Tier 1 2025 Shift-2 📅 06 Jun, 2025

Surendra has 102 litres of Oil A and 224 litres of Oil B. He fills a number of identical containers with the two types of oil in a manner that each container has only one type of oil, and all containers are completely filled. What can be the maximum volume (in litres) of each container that Surendra uses, so that all the oil that Surendra has, of both the types, can be poured into these containers?

A
1
B
8
C
9
D
2
Result Summary
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NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-2
Surendra has 102 litres of Oil A and 224 litres of Oil B. He fills a number of identical containers with the two types of oil in a manner that each container has only one type of oil, and all containers are completely filled. What can be the maximum volume (in litres) of each container that Surendra uses, so that all the oil that Surendra has, of both the types, can be poured into these containers?
Correct Answer
2
Mathematical Concept: The problem asks for the largest identical container size that can exactly measure out two different total volumes without mixing them. Th......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic HCF & LCM
Pg. No -
💡 Analysis & Explanation
Mathematical Concept ▼
The problem asks for the largest identical container size that can exactly measure out two different total volumes without mixing them. This requires finding the Highest Common Factor (HCF) of the two volumes.
Prime Factorization ▼
Break down the given quantities into prime factors. 102 = 2 × 3 × 17. For the second quantity, 224 = 2 × 112 = 2 × 2 × 56 = 2^5 × 7.
Extracting the HCF ▼
Compare the prime factors of both numbers. The only common prime factor between 102 and 224 is the number 2.
Conclusion ▼
The highest common factor is 2, meaning a 2-litre container is the maximum possible size.
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