Question
Download Solution PDFFind the largest number by which dividing 310, 550 and 728 gives the same remainder.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Numbers: 310, 550, 728
Calculation:
Let the required number be N. When each number is divided by N, they leave the same remainder.
Step 1: Subtract the smaller numbers from the larger ones.
550 - 310 = 240
728 - 550 = 178
728 - 310 = 418
Step 2: Find the HCF of 240, 178, and 418.
Prime factorization:
240 = 2 × 2 × 2 × 2 × 3 × 5
178 = 2 × 89
418 = 2 × 11 × 19
Step 3: Identify the common factors.
The common factor is 2.
Step 4: The HCF is 2.
⇒ The greatest number is 2.
∴ The greatest number is 2
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