For numbers less than 40, what are the pairs of numbers that have a GCF of 12
To find pairs of numbers that have a Greatest Common Factor (GCF) of 12, we can methodically go through all numbers less than 40 and check if they have a GCF of 12 with any other number.
First, let's find the prime factorization of 12. The prime factorization of 12 is 2^2 × 3.
Now, let's go through the numbers less than 40 and see if their prime factorization includes at least two 2's and one 3. These are the pairs that will have a GCF of 12:
1) 12: Since 12 is a multiple of 12 and has the same prime factorization, it has a GCF of 12 with itself.
2) 24: The prime factorization of 24 is 2^3 × 3. Since it has at least two 2's and one 3, it has a GCF of 12 with 12.
3) 36: The prime factorization of 36 is 2^2 × 3^2. Again, it has at least two 2's and one 3, so it has a GCF of 12 with both 12 and 24.
Therefore, the pairs of numbers less than 40 that have a GCF of 12 are (12, 12), (12, 24), and (12, 36).