SAN FRANCISCO — In a companywide meeting earlier this year, Mark Zuckerberg was asked if Instagram could have hit one billion users if it had not been bought by Facebook.

Probably not, he said. At least, not as quickly.

But at a later meeting a mile or so down the road at Instagram’s headquarters in Menlo Park, Calif., a few streets, interestingly enough, off a thoroughfare called Independence Drive, the popular photo-sharing app’s co-founders, Kevin Systrom and Mike Krieger, had a slightly different answer to that question.

Perhaps. Eventually.

We will never know who was right. But we will know soon enough what Instagram will be like without its co-founders. On Monday evening, Mr. Systrom, Instagram’s chief executive, and Mr. Krieger, its chief technology officer, abruptly announced they would leave the company, though they did not give a specific date.

No one thing led to their decision to part ways with Facebook, which acquired Instagram for $1 billion in 2012. But little things added up over time: disagreements over tweaks to their product, staffing changes and how over the last year Mr. Zuckerberg asserted more control over their business, which had essentially operated independently inside Facebook.