Given the GCM or LCM, what else do you know about each pair of numbers? Two numbers have a GCF of 2
one is a power of 2, one is an odd multiple of 2.
One is the power of 2 one is an even #of 2
If two numbers have a greatest common factor (GCF) of 2, there are a few things we can infer about the pair of numbers.
1. Divisibility: Both numbers are divisible by 2. In other words, they are both even numbers.
2. Prime Factorization: When we find the prime factorization of each number, we will see that both numbers have at least one factor of 2 in common.
3. LCM: The least common multiple (LCM) of two numbers with a GCF of 2 will be at least twice the value of the larger number. This happens because if both numbers have a factor of 2 in common, we only need to consider the other prime factors when finding the LCM. Thus, the LCM will be larger than or equal to the product of 2 and the larger number.
For example, let's consider two numbers: 16 and 18.
The GCF of 16 and 18 is 2, which means both numbers are divisible by 2. The prime factorization of 16 is 2 * 2 * 2 * 2, and the prime factorization of 18 is 2 * 3 * 3. Both numbers have a factor of 2 in common.
To find the LCM, we compare the prime factors: 2 * 2 * 2 * 2 * 3 * 3 = 144. The LCM of 16 and 18 is 144, which is greater than twice the larger number (18).
In summary, if two numbers have a GCF of 2, we can conclude that they are both even, they share at least one factor of 2 in their prime factorization, and the LCM will be larger than or equal to twice the value of the larger number.