Answer:
a) To find the Highest Common Factor (HCF) of 75, 90, and 120, you can list the factors of each number and identify the largest factor that they all share.
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 90: 1, 2, 3, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The largest factor that all three numbers share is 15. Therefore, the HCF of 75, 90, and 120 is 15.
b) Bhu's alarm starts at 09:10 and sounds every 12 minutes. Dax's alarm starts at 09:30 and sounds every 8 minutes.
We can find the times when their alarms will sound simultaneously by finding a common multiple of both 12 and 8 after 09:30.
The multiples of 12 are: 12, 24, 36, 48, 60, ...
The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...
The first time after 09:30 that both alarms will sound at the same time is 09:36.
Therefore, the first time after 09:30 that both Bhu's and Dax's alarms will sound at the same time is 09:36.
Explanation: