For numbers less than 40, list each pair of numbers that has a greatest common factor (GCF) of 12.
36 & 36
36 & 24
36 & 12
24 & 24
24 & 12
12 & 12
To find pairs of numbers less than 40 that have a greatest common factor (GCF) of 12, we can consider the factors of 12 and then check which pairs have common factors other than 1.
The factors of 12 are 1, 2, 3, 4, 6, and 12. For a pair of numbers to have a GCF of 12, they must have a common factor of 12. We can use this information to identify the pairs by multiplying each of the factors by various numbers.
Let's go through the factors:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
4 x 3 = 12
6 x 2 = 12
12 x 1 = 12
Now, we need to see if these pairs have a GCF of 12. To do that, we consider whether there are any additional common factors other than 1.
For example, let's take the pair (2, 6). We list out the factors of both numbers:
Factors of 2: 1, 2
Factors of 6: 1, 2, 3, 6
The common factors of 2 and 6 are 1 and 2. Since there are no other common factors, the GCF is 2.
By applying the same process to each pair, we can determine the GCF for all the pairs of numbers less than 40.