Question
Which of the following is the greatest number that
divides 72 and 119 and leaves 3 and 4 as respective remainders?Solution
To find the greatest number that divides 72 and 119 and leaves remainders 3 and 4, respectively, follow these steps: Adjust the numbers by subtracting the remainders: 72 - 3 = 69 119 - 4 = 115 Find the greatest common divisor (GCD) of 69 and 115. Use the Euclidean algorithm: 115÷69=1 (quotient),115−69=46 69÷46=1 (quotient),69−46=23 46÷23=2 (quotient),46−46=0 The GCD is 23. Thus, the greatest number that divides both 72 and 119, leaving remainders 3 and 4, respectively, is 23.
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