In 24 hours, the hour hand will pass through a number multiple of 8 times.
The hour hand of an analog clock completes a full rotation every 12 hours.
Since there are 4 numbers on a clock face that are multiples of 3 (3, 6, 9,
and 12), the hour hand will pass through a number multiple of 3 4 times in
12 hours.
Therefore, in 24 hours, the hour hand will pass through a number multiple of 3 4 * 2 = 8 times.
Question
How many times a day does the hour hand of an analog clock pass through a number multiple of 3?