What is the greatest common factor of 10 and 30?
a. 40
b. 30
c. 20
d. 101
The correct answer and explanation is:
The correct answer is b. 30.
The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder.
To find the GCF of 10 and 30, follow these steps:
- List the factors of each number:
- The factors of 10 are: 1, 2, 5, 10.
- The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
- Identify the common factors:
The common factors of 10 and 30 are: 1, 2, 5, 10. - Find the greatest common factor:
The greatest of the common factors is 10.
Thus, the GCF of 10 and 30 is 10. However, none of the options (a. 40, b. 30, c. 20, d. 101) match the correct answer, which suggests that there might be a mistake in the question choices or intended context. Based on the process of finding the GCF, 10 would be the correct answer, though it isn’t listed in the options provided.