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As you see in datasheet of Atmega32A, it says that the bits ADPS of register ADCSRA are controlling the Prescaler of the ADC clock by dividing the frequency of external crystal on some division factor, what if I am depending on the internal oscillator and don't have an external crystal, do these bits still work?!

ADPS bits of ADCSRA register

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Yes it will divide the CPU frequency, no matter what is the clock source.

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