Answer:
6
Step-by-step explanation:
Let n be unknown divisor and a be the same remainder, then
[tex]63=q_1\cdot n+a\\ \\45=q_2\cdot n+a\\ \\69=q_3\cdot n+a[/tex]
Subtract a from all equalities:
[tex]63-a=q_1\cdot n\\ \\45-a=q_2\cdot n\\ \\69-a=q_3\cdot n[/tex]
Subtract them:
[tex]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[/tex]
The greatest number is 6. When you divide numbers 63, 45, 69 by 6, you'll get remainders 3, 3, 3, respectively.
