Question
Download Solution PDFWhat is the greatest number that will divide 446 and 487, leaving remainders 9 and 12, respectively?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number 1: 446, leaving remainder 9.
Number 2: 487, leaving remainder 12.
Formula Used:
To find the greatest number that divides two given numbers leaving specific remainders, subtract the remainders from each number and then find the GCD (Greatest Common Divisor) of the results.
Calculation:
Number 1 - Remainder 1 = 446 - 9
Number 2 - Remainder 2 = 487 - 12
⇒ 446 - 9 = 437
⇒ 487 - 12 = 475
Now find the GCD of 437 and 475.
437 = 19 × 23
475 = 19 × 25
GCD (437, 475) = 19
The greatest number that will divide 446 and 487 leaving remainders 9 and 12 respectively is 19.
Last updated on Jun 2, 2025
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