Question
Download Solution PDFThe greatest number that divides 38, 45 and 52 leaves remainders 2, 3 and 4 respectively is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Numbers: 38, 45, 52
Remainders: 2, 3, 4
Formula used:
To find the greatest number that divides these numbers leaving specific remainders:
Required number = HCF of (38 - 2), (45 - 3), (52 - 4)
Calculation:
38 - 2 = 36
45 - 3 = 42
52 - 4 = 48
Finding HCF of 36, 42, and 48:
Prime factors of 36: 2 × 2 × 3 × 3
Prime factors of 42: 2 × 3 × 7
Prime factors of 48: 2 × 2 × 2 × 2 × 3
Common factors: 2 × 3 = 6
⇒ HCF = 6
The greatest number that divides 38, 45, and 52, leaving remainders 2, 3, and 4, respectively, is 6.
∴ The correct answer is option (3).
Last updated on May 26, 2025
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