Must the specific invocations be recited a certain number of times consecutively, or can they be broken up into different periods throughout the day?

The preferred way to perform remembrances (adhkar) is consecutively, even though continuity is not a condition for receiving the reward. It is mentioned in a hadith that whoever recites "La ilaha illallah wahdahu la sharika lah, lahul mulku wa lahul hamdu wa huwa 'ala kulli shayin qadeer" (There is no god but Allah, alone, without partner. To Him belongs sovereignty and to Him belongs praise, and He is over all things competent) one hundred times in a day, will have a great reward. Similarly, whoever recites "Subhanallah wa bihamdihi" (Glory be to Allah and praise be to Him) one hundred times, his sins will be forgiven. Imam An-Nawawi mentioned that the stated reward is attained by reciting the remembrance one hundred times in a day, whether consecutively or separately. However, it is preferable for them to be consecutive at the beginning of the day so that the remembrance serves as a protection throughout the day.