Maths challenge

My son was given this challenge for his school homework tonight:

Pick a number in the range 2-100. Next, pick a number that is a factor or a multiple of the first, again using only the numbers 2-100. Continue like this, building a chain of numbers in the range 2-100 in which each number is either a factor or a multiple of its predecessor in the chain. What is the longest non-repeating chain you can build?

I feel some gentle programming about to occur…

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