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Python 2, (削除) 220 (削除ここまで) (削除) 202 (削除ここまで) (削除) 195 (削除ここまで) 183 bytes

g=lambda a,b:a and g(b%a,a)or b;n,d=input();m=c=()
while n+d>2:
 t=n*d;f=p=2
 while t>p:
	if t%p:p+=1;f*=p
	else:t/=p
 if n%p:c+=p,;n*=f
 else:m+=p,;d*=f
 t=g(n,d);n/=t;d/=t
print m,c

Try it online! Edit: Saved (削除) 18 (削除ここまで) 25 bytes thanks to @Mr.Xcoder. Saved 12 bytes thanks to @JonathanFrech.