What is the greatest number that will divide 446 and 487, leaving remainders 9 and 12, respectively?

Given:

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.