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There is no fixed answer to this question as it depends on various factors during the development as well as operation stage for apps like Instagram. In the initial launch of the Instagram app itself, there might be only 1-2 UI/UX designers but Instagram has developed a lot over the years, so they require a team of hundreds of designers now.
Factors affecting the size of the development team
1. Target Audience Size
2. Target Service Area
3. Number and Complexity of features
4. Target Launch Date
To know more about the complete development process you can also visit How to create an app like Instagram and know how much it cost?