An enormous great white shark – believed to be one of the biggest on record – has been spotted off the coast of Hawaii by divers who took a swim with the predator.

The six-metre (20-foot) female shark – bearing similar markings as “Deep Blue”, the largest great white shark recorded – made its surprise appearance on Tuesday, joining other sharks feasting on a sperm whale carcass off Oahu.

“We saw a few [tiger sharks] and then she came up and all the other sharks split and she started brushing up against the boat,” said Ocean Ramsey, one of the divers, recounting the extraordinary encounter to the Honolulu Star Adviser.

“She was just this big beautiful gentle giant wanting to use our boat as a scratching post,” added Ramsey, who swam with the shark all day and captured stunning pictures. “We went out at sunrise, and she stayed with us pretty much throughout the day.”

Ramsey said the animal, believed to be at least 50 years old and weighing an estimated 2.5 tonnes, was “shockingly wide” and may be pregnant.

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Sightings of great white sharks are rare in Hawaii, where the water is too warm.