Do the six days of Shawwaal have to be fasted consecutively?

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Check below answers in case you are looking for other related questions:
The reason why it is not allowed to fast on Saturdays
Fasting on his birthday and on the birthday of the Prophet (blessings and peace of Allah be upon him)

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Related Answers:
Is it mustahabb to observe fasts in expiation for breaking an oath as the six days of Shawwaal?
He had intercourse with his wife when she was observing a voluntary fast
Fasting on Saturdays
The reason why it is not allowed to fast on Saturdays
Fasting on his birthday and on the birthday of the Prophet (blessings and peace of Allah be upon him)

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