two numbers greater than 40 that have 2 and 3 as their only prime factors.
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it is 54 48
The answer is 48 and 54
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48 and 54 because they are the only ones I could find
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To find two numbers greater than 40 that have 2 and 3 as their only prime factors, we need to look for numbers that are multiples of these primes.
Step 1: Start by finding the multiples of 2 and 3 greater than 40.
- Multiples of 2: 42, 44, 46, ...
- Multiples of 3: 45, 48, 51, ...
Step 2: Check each number to see if it only has 2 and 3 as prime factors.
- For example, let's consider 42. To determine its prime factors, we can divide it by the smallest prime number (2) repeatedly until we cannot divide it further:
- 42 รท 2 = 21
- 21 รท 2 = 10.5 (not a whole number)
- Since we were able to divide 42 only by 2, we can conclude that it has 2 as one of its prime factors.
- To check if it also has 3 as a prime factor, we can apply the same process of division repeatedly:
- 42 รท 3 = 14
- 14 รท 3 = 4.67 (not a whole number)
- Since we couldn't divide 42 by 3, we can conclude that it doesn't have 3 as a prime factor.
Step 3: Repeat Step 2 for each multiple of 2 and 3 that we found in Step 1 until we find two numbers that satisfy the condition.
Let's go through the process:
Multiples of 2: 42, 44, 46, 48, ...
Out of these, let's check 42:
42 รท 2 = 21
21 รท 2 = 10.5 (not a whole number)
42 does not satisfy our condition since it has a prime factor other than 2 and 3.
Now let's move to the multiples of 3: 45, 48, 51, 54, ...
Out of these, let's check 45:
45 รท 2 = 22.5 (not a whole number)
45 does not satisfy our condition since it has a prime factor other than 2 and 3.
We continue this process until we find two numbers that meet the criteria. In this case, there are no numbers greater than 40 that have 2 and 3 as their only prime factors.