ASX dividend shares can be great investments. However, there's a particular factor that I look for the most when it comes to passive income.

When it comes to businesses that pay dividends, there are various elements to consider. How big is the dividend yield? What industry is the business from? How often is the dividend growing?

Businesses like BHP Group Ltd (ASX: BHP), Rio Tinto Ltd (ASX: RIO), and Fortescue Ltd (ASX: FMG) typically pay a large dividend yield, though their payout can be (and is) regularly reduced because of the volatility of commodity prices.

Meanwhile, businesses like ANZ Group Holdings Ltd (ASX: ANZ), Westpac Banking Corp (ASX: WBC), and National Australia Bank Ltd (ASX: NAB) may also offer a high yield, but they have not grown their earnings and share prices over the past decade.

If I were relying on passive income from ASX dividend shares, there's one element that would most attract me.

Dividend growth is key

For me, a growing dividend is a great sign of a business going in the right direction.

Firstly, if the dividend is growing, then it's not going backwards. If the business has a track record of increasing its dividend, then there's a good chance it could continue this performance, particularly if it's in a fairly consistent industry.

Second, we've seen a lot of inflation in the last few years. Dividend growth can help offset the negative effects of a higher cost of living.

Third, if a dividend is being (sustainably) increased, that implies the underlying profit is going up too. I believe profit growth is the key to justify a higher share price, so a business with a rising dividend could deliver capital growth too.

When I think about which ASX dividend shares tick those boxes right now, then Washington H. Soul Pattinson and Co. Ltd (ASX: SOL) and Brickworks Ltd (ASX: BKW) are among the best.

Other businesses that have delivered impressive dividend growth include TechnologyOne Ltd (ASX: TNE), Sonic Healthcare Ltd (ASX: SHL), and Coles Group Ltd (ASX: COL).

Pro Medicus Ltd (ASX: PME) and WiseTech Global Ltd (ASX: WTC) have also delivered huge revenue, profit, and dividend growth, though their dividend yields are now exceptionally low because of the capital growth (which pushes down the yield for new investors).

I like the prospects of the above businesses to keep growing payouts and their share prices.