To find all the factors of 40, we'll determine which numbers between 1 and 40 divide 40 evenly without leaving a remainder. Let's do this step by step:
1. Start with 1:
[tex]\( 40 \div 1 = 40 \)[/tex] with no remainder, so 1 is a factor.
2. Next, check 2:
[tex]\( 40 \div 2 = 20 \)[/tex] with no remainder, so 2 is a factor.
3. Next, check 3:
[tex]\( 40 \div 3 = 13.33 \)[/tex] which leaves a remainder, so 3 is not a factor.
4. Next, check 4:
[tex]\( 40 \div 4 = 10 \)[/tex] with no remainder, so 4 is a factor.
5. Next, check 5:
[tex]\( 40 \div 5 = 8 \)[/tex] with no remainder, so 5 is a factor.
6. Next, check 6:
[tex]\( 40 \div 6 = 6.66 \)[/tex] which leaves a remainder, so 6 is not a factor.
7. Next, check 7:
[tex]\( 40 \div 7 = 5.71 \)[/tex] which leaves a remainder, so 7 is not a factor.
8. Next, check 8:
[tex]\( 40 \div 8 = 5 \)[/tex] with no remainder, so 8 is a factor.
9. Next, check 9:
[tex]\( 40 \div 9 = 4.44 \)[/tex] which leaves a remainder, so 9 is not a factor.
10. Next, check 10:
[tex]\( 40 \div 10 = 4 \)[/tex] with no remainder, so 10 is a factor.
11. Next, check 11 through 19:
These numbers will all leave a remainder when dividing 40.
12. Next, check 20:
[tex]\( 40 \div 20 = 2 \)[/tex] with no remainder, so 20 is a factor.
13. Finally, check 40:
[tex]\( 40 \div 40 = 1 \)[/tex] with no remainder, so 40 is a factor.
Therefore, the complete list of factors of 40 is:
[tex]\[ 1, 2, 4, 5, 8, 10, 20, 40 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{1, 2, 4, 5, 8, 10, 20, 40} \][/tex]
