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Find the largest number that divides 220, 313, and 716, leaving a remainder of 3 in each case.

Answer :

Final answer:

The largest number that can divide 220, 313 and 716 leaving a remainder of only 3 in each case is 1. This is determined by finding the greatest common divisor (GCD) of (220-3), (313-3), and (716-3) - which are the original numbers after subtracting the remainder.

Explanation:

The given numbers are 220, 313, and 716, from which a remainder of 3 is left when divided by some unknown number. Thus, the numbers 220-3=217, 313-3=310, and 716-3=713 would all be divisable by the same unknown number. This is because subtracting the remainder provides us the original numbers that were divided. The unknown number we're seeking for is a common divisor of these three results.

To find this common divisor, calculate the greatest common divisor (GCD) of the three numbers 217, 310, and 713. The GCD is the largest number that can divide these three numbers without leaving a remainder. The GCD of 217, 310, and 713 is 1. Therefore, the largest number that divides 220, 313, 716 leaving a remainder of 3 is in fact 1.

Learn more about Greatest Common Divisor here:

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