To determine all the factors of 10, let's first understand what a factor is. Factors of a number are all the integers that can be multiplied together to produce that number. In simpler terms, a factor of 10 is any number that divides 10 evenly without leaving a remainder.
Here's the step-by-step breakdown of how to find the factors of 10:
1. Start with the number 1. Since [tex]\(1 \times 10 = 10\)[/tex], 1 is a factor of 10.
2. Next, consider the number 2. Since [tex]\(2 \times 5 = 10\)[/tex], 2 is a factor of 10.
3. Now look at the number 3. 3 cannot be multiplied by any integer to result in 10, so 3 is not a factor.
4. Consider the number 4. Similar to 3, 4 cannot evenly divide 10, leaving it not a factor.
5. Move to the next number, 5. Since [tex]\(5 \times 2 = 10\)[/tex], 5 is a factor of 10.
6. Lastly, the number 10 itself. Since [tex]\(10 \div 10 = 1\)[/tex] and [tex]\(1 \times 10 = 10\)[/tex], 10 is indeed a factor of itself.
Now, let's compile all the factors we have found:
- 1
- 2
- 5
- 10
So, the complete list of factors of 10 is [tex]\(1, 2, 5,\)[/tex] and [tex]\(10\)[/tex].
Comparing this list with the answer choices provided:
- Choice A states 2, 5 – This is incomplete.
- Choice B states 1, 2, 5 – This is still incomplete.
- Choice C states 1, 2, 5, 10 – This is correct.
- Choice D states 1, 10 – This is incomplete.
Therefore, the correct answer is:
C. 1, 2, 5, 10
