The view that is most likely to be correct is that of the majority of scholars, which is that a dog’s saliva is impure (najis), and it is not permissible to pray in a garment on which there is anything of a dog’s saliva, until it has been purified in the manner explained above. As for the view of the Malikis, that a dog’s saliva is pure, and there is no blame on the one who prays wearing that garment [on which there is some dog’s saliva, and his prayer is valid, and he does not have to do anything, if someone follows this view [of Malik] because he is satisfied with the evidence, or he follows the view of one of the imams or scholars who hold that view, then he is not to be denounced, because the difference of opinion regarding this matter is an acceptable difference of opinion, and each group has its evidence which it believes supports its view.

The ruling on the urine and faeces of a dog is the same as the ruling on all other impurities. What is required to purify it is to wash the item until the impurity disappears. As for washing it seven times, that applies specifically to the dog’s saliva only, as mentioned in the hadith.

Nothing in your house should be deemed impure unless you know for certain that this man touched it, and that his hands were still wet when he touched it and the dog’s saliva had not yet dried up, or he touched something wet when there was still a trace of saliva on his hands. For more details, please see the long answer.