How many types of auxiliary are there?

In English there are two types of auxiliary verb, primary auxiliaries and modal auxiliaries. The three primary auxiliary verbs are 'be', 'have' and 'do'. There are ten common modal auxiliary verbs and they are 'can', 'could', 'will', 'would', 'shall', 'should', 'may', 'might', 'must' and 'ought'.
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