Final answer:
The GCF of -66 and 110 is 22, disregarding the negative sign for the purpose of finding factors. The LCM is calculated using the relationship between GCF and LCM, resulting in 330. Both results are obtained through mathematical operations involving the absolute values of the numbers.
Step-by-step explanation:
To find the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of -66 and 110, we start by finding the GCF. The GCF is the largest number that divides both numbers. Since the sign does not affect the divisibility, we can ignore it and find the GCF of 66 and 110.
We list the factors of each number:
- Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
- Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110
The largest common factor is 22.
Now for the LCM, which is the smallest number that both -66 and 110 can divide into evenly. We use the relationship between GCF and LCM, which is:
GCF × LCM = the absolute value of the product of the two numbers.
So, we calculate the LCM as follows:
LCM = |product of the two numbers| / GCF
LCM = |(-66) × 110| / 22
LCM = 7260 / 22
LCM = 330
Therefore, the GCF of -66 and 110 is 22 and the LCM is 330.