What is the greatest number that leaves remainder (5) when dividing (137), (185), and (257)?
Answer and explanation
Correct answer: (12)
Step 1: Subtract the remainder (5) from each number to get (132), (180), and (252). Step 2: Find their HCF. (132=2^2\times 3\times 11), (180=2^2\times 3^2\times 5), (252=2^2\times 3^2\times 7), so the common part is (2^2\times 3=12). Step 3: In same-remainder problems, subtract the remainder first.
Frequently asked questions
What is the correct answer to this question?
(12)
Why is this the correct answer?
Step 1: Subtract the remainder (5) from each number to get (132), (180), and (252). Step 2: Find their HCF. (132=2^2\times 3\times 11), (180=2^2\times 3^2\times 5), (252=2^2\times 3^2\times 7), so the common part is (2^2\times 3=12). Step 3: In same-remainder problems, subtract the remainder first.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: HCF and LCM using prime factorisation.
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