According to research analysing 150,000 brand posts on Instagram, the optimal number of hashtags per image is:
There is only one hash tag: %+2%
Two hash tags: 2.6% up
+6%, #hashtags, and #shares
+8.9% with 4 hashtags
Five hash tags: an additional 12%.
With only six hashtags, the increase is 17.5 percent.
+23% with 7 hashtags
+21.4% with 8 hashtags
With an increase of 6.5% for using 9 hashtags
Source: https://socialfresh.com/tip-the-secret-sauce-of-instagram-hashtags/