Is there a relationship between the divisibility and factors of a number? Explain your answer and give an example to illustrate your reasoning. (3 points)
Yes, there is a relationship between the divisibility and factors of a number. The divisibility of a number determines if it can be divided evenly by another number, while the factors of a number are the numbers that evenly divide into it.
If a number is divisible by another number, then the divisor is a factor of the original number. In other words, if a number can be divided evenly by a certain divisor, then that divisor is one of the factors of the original number.
For example, let's take the number 12. It is divisible by both 2 and 3 because it can be evenly divided by each of them. Therefore, both 2 and 3 are factors of 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. This means that 12 can be evenly divided by any of these numbers, which are all factors of 12.
In conclusion, the divisibility of a number determines if it can be evenly divided by another number, while the factors of a number are the numbers that evenly divide into it. So, if a number is divisible by a certain number, then that divisor is a factor of the original number.