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Step-by-step explanation:
Co-prime numbers are numbers that only have 1 as a common factor.
For example, 35 = 1×5×7, and 39 = 1×3×13. So 35 and 39 are co-prime.
Write the prime factorization of each number:
17 = 1×17
25 = 1×5²
35 = 1×5×7
43 = 1×43
55 = 1×5×11
119 = 1×7×17
187 = 1×11×17
43 is co-prime with all of these, so we will not use it.
If we start with 35 in the upper left, and 187 in the lower right, then we can also rule out 17 and 25, since these are co-prime with either 35 or 187.
So that leaves 55 and 119 as the other two numbers. They can go in any order, as long as they are diagonal from each other.