why does an A380 have 4 engines but carrys nearly twice as much as a 747 which also has 4 engines? why does an A340 have 4 engines but a777 has 2 engines but has a longer range and the difference in payload is not very much? the 707,727 and the 737 have more or less the same range and payload but they have4,3 and 2 engines respectively. why does the 787 have 2 engines and is faster and uses less fuel? who knows about the A350 or the 747-8?

Each engine has its own thrust rating. Weight VS Thrust is the main thing here. While you did see more engines, its does not mean more thrust. The 2 engines on the 777 are a huge diameter ( Not sure exactly) and therefore have a huge thrust rating. The A380 has less thrust per engine, compared to the 777.

General rule, fewer but larger engines will always be more fuel efficient.

One great big engine would be even better, but we want multi-engine for safety.

3-engine planes were designed during a time when twin-engine aircraft could not get certified for extended overwater operation.

Sometimes more power is needed for taking off on shorter runways, like for example Santa Fe. Sometimes more power is needed for steeper climb, to comply with noise abatement legislation like at Orange County.

Technological advances have made it possible to replace 3- & 4-engine designs with twin-engine aircraft.

A380 & 747 r designs ages apart. The 380 is the most recent & the 747 nearly 40 years old. Technological advancements endowed the A380 with advantages which did not exist earlier, hence twice the payload. The differences in payloads & range which r notable in the later generation of aircraft merely reflect the advent of technology.
Since some years, the time between failures in modern jet engines has dropped down so much that 3 & 4 engines have become redundant. Fuel efficiency has improved & structures become much lighter. All this has dictated the current designs which u r seeing & is the underlying point of ur question.

Ok the main reason is for emergency. For example if the A340 had an engine that failed it would still have 3 engines to fly with. If the A340 had two engines & one failed, it would not be able to fly. When the aircraft has four engines & loses one, it only loses 25% of the power, instead of losing 50% if it has two. The 777 & other twin engine aircraft r able to fly with just one engine. The 787 is an engineering marvel. It was made from composite material so it is way lighter than an aircraft of the similar size. l believe it has almost 20% better efficiency, this is due to better aerodynamics, better engines, & less weight. 20% efficiency can make a major difference in aircraft.

Different engines have different thrust ratings that r needed to power different planes.. The A380 carries more than the 747 but still uses 4 engines cus each of its one engines r more powerful than the 747's: 60,000lbs of thrust to 70,000lbs. The A340 has 4 engines cus when it was made, there were no engines powerful enough to provide all the thrust it needed with two engines. the 777 might have less engines, but each of its engines has far more thrust than one A340 engines. A single 777 engines has 115,000lbs of thrust while an A340 has 65,000. So with extra fuel tanks & more powerful engines, the 777 can have less engines but still fly farther than the A340.
The 787 due to composites which r lightweight & fuel efficient will make it the most efficient jet when its starts flying & also due to new engines technology like the GeNx & Trent 1000, can cruise faster than other planes.
The 747-8 will still remain a 4engines plane like its predecessors while the A350 is a two engined plane, but each of its engines will have more thrust than one 747-8 engine.