Pablo found that his uncle’s age can be divided by three different prime numbers. What are three possible ages of his uncle? Show your work.
so, start with the smallest 3 primes: 2*3*5=30
So, any multiple of 30 can be divided by those three primes.
Try using other primes, and see what you think ...
To find three possible ages of Pablo's uncle that can be divided by three different prime numbers, we can start by listing the prime numbers and their multiples until we find three distinct ages for his uncle.
The first three prime numbers are 2, 3, and 5. Let's consider their multiples:
- Multiples of 2: 2, 4, 6, 8, 10, 12, ...
- Multiples of 3: 3, 6, 9, 12, 15, ...
- Multiples of 5: 5, 10, 15, 20, ...
From these lists, we observe that the number 6 appears as a multiple of both 2 and 3. Therefore, 6 can be one possible age of Pablo's uncle.
Now let's consider other combinations:
- Multiples of 2 and 5: 10, 20, 30, ...
- Multiples of 3 and 5: 15, 30, 45, ...
From these lists, the number 30 appears as a multiple of both 2 and 5. Therefore, 30 can be another possible age of Pablo's uncle.
Lastly, let's consider the multiples of 3 and other prime numbers greater than 5:
- Multiples of 3 and 7: 21, 42, 63, ...
- Multiples of 3 and 11: 33, 66, 99, ...
From these lists, the number 66 appears as a multiple of both 3 and 11. Therefore, 66 can be the third possible age of Pablo's uncle.
To summarize, three possible ages of Pablo's uncle that can be divided by three different prime numbers are 6, 30, and 66.