One key theme that has driven investors to become increasingly optimistic about Apple (NASDAQ:AAPL) stock recently has been the tech giant's momentum in services. That fast-growing business unit has become a substantial driver of both revenue and profits for the world's largest tech company.

In Apple's recently reported blowout fiscal first quarter, its services business continued to fire on all cylinders. The segment's momentum further validated the company's ongoing transition toward more predictable revenue streams. In addition, its broad services offerings are fortifying the company's competitive advantage by more firmly entrenching customers in Apple's ecosystem.

To see just how strong Apple's services business is now, consider these six figures.

Apple senior vice president of software engineering Craig Federighi unveils iOS 13 at WWDC 2019

Apple senior vice president of software engineering Craig Federighi. Image source: Apple.

$12.7 billion

Total services revenue in the fiscal first quarter, which ended Dec. 28, was a record $12.7 billion, up 17% from $10.9 billion in the year-ago period. This equates to an annualized revenue run-rate of more than $50 billion.

The growth in services revenue was broad-based.

"Once again, we saw double-digit growth in all five of our geographic segments and established new all-time records for multiple categories," said Apple CEO Tim Cook during the earnings call, "including cloud services, music, payment services, and our App Store search ad business, as well as setting a December quarter record for the App Store and Apple Care."

The segment is also growing as a percentage of Apple's total revenue. It accounted for 18% of trailing-12-month revenue, up from 13% of annual revenue two years ago.

64.4%

But services' share of revenue understates its importance to Apple's business. The segment has an outsize impact on the tech company's bottom line because it boasts a much higher gross margin than hardware. Services gross margin in fiscal Q1 was 64.4%, compared to a 34.2% gross margin on hardware.

100 million monthly active users

Apple News, one of Apple's more mature services, now boasts over 100 million monthly active users in the U.S., U.K., Australia, and Canada combined.

15 billion transactions

Another well-established service, Apple Pay, continues to grow at an extraordinary rate. Revenue and transactions from Apple Pay "more than doubled year-over-year with a run-rate exceeding 15 billion transactions a year," Cook said during the earnings call.

480 million paid subscriptions

Subscriptions to Apple's services and third-party apps continue to be a key catalyst. Total paid subscriptions to iOS apps reached 480 million during the quarter -- up 120 million from the year-ago period. Subscriptions to third-party apps grew particularly fast, rising 40% year over year.

Management said during the earnings call that it expects subscriptions to hit 600 million by the end of fiscal 2020.

1.5 billion active devices

Perhaps the most bullish metric regarding the future of Apple's services business is its installed base of 1.5 billion active devices. That's up by more than 100 million from this time last year. Growth in active devices means Apple has more customers tied into its ecosystem of hardware, software, and services, which gives the company more opportunities to monetize its user base and fuel further growth.

Editor's note: This article has been corrected. Apple reported 480 million paid subscriptions.