This statement is false: If a number has 2 and 6 as factors, then it has 12 as a factor. Which of the following numbers prove this statement false
12 equals 2 times 6
To prove the statement false, we are looking for a number that has 2 and 6 as factors but does not have 12 as a factor.
Let's consider the number 18.
Step 1: Check if 18 has 2 as a factor.
- 18 ÷ 2 = 9, so 2 is a factor of 18.
Step 2: Check if 18 has 6 as a factor.
- 18 ÷ 6 = 3, so 6 is a factor of 18.
Step 3: Check if 18 has 12 as a factor.
- 18 ÷ 12 = 1.5, so 12 is not a factor of 18.
Therefore, the number 18 proves the statement false since it has 2 and 6 as factors but does not have 12 as a factor.
To verify if the statement is false, we need to find a number that has 2 and 6 as factors but does not have 12 as a factor.
To do this, we can start by listing the factors of both 2 and 6:
Factors of 2: 1, 2
Factors of 6: 1, 2, 3, 6
Now, we need to find a number that has common factors with both 2 and 6 but does not have 12 as a factor. We can find such a number by multiplying one or more factors of 2 with factors of 6.
Let's try multiplying 2 with each factor of 6:
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 6 = 12
As we can see, when we multiply 2 with each factor of 6, we do get the number 12. However, the statement asks for a number that does not have 12 as a factor.
Let's try multiplying a factor of 2 with a different factor of 6:
1 x 3 = 3
When we multiply 1 and 3, we get the number 3. This number has 2 and 6 as factors (since those are the factors we used to obtain 3), but it does not have 12 as a factor.
Therefore, the number 3 is an example that proves the statement false.