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Neko [114]
2 years ago
8

Find the greatest number that will divide 63, 45 and 69 so as to leave the same remainder.

Mathematics
1 answer:
jeka57 [31]2 years ago
7 0

Answer:

6

Step-by-step explanation:

Let n be unknown divisor and a be the same remainder, then

63=q_1\cdot n+a\\ \\45=q_2\cdot n+a\\ \\69=q_3\cdot n+a

Subtract a from all equalities:

63-a=q_1\cdot n\\ \\45-a=q_2\cdot n\\ \\69-a=q_3\cdot n

Subtract them:

63-45=(q_1-q_2)n\Rightarrow 18=(q_1-q_2)n\\ \\69-63=(q_3-q_1)n\Rightarrow 6=(q_3-q_1)n\\ \\69-45=(q_3-q_2)n\Rightarrow 24=(q_3-q_2)n

The greatest number is 6. When you divide numbers 63, 45, 69 by 6, you'll get remainders 3, 3, 3, respectively.

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