Certainly! To find the factors of 40, we need to determine all the numbers that can divide 40 without leaving a remainder. Here is how we can do this step-by-step:
1. Identify the smallest factor:
Always start with 1. The number 1 is a factor of every number.
- 1 is a factor of 40 because [tex]\( 40 \div 1 = 40 \)[/tex].
2. Identify the next smallest factor:
The next smallest factor will be the smallest prime number, which is 2.
- 2 is a factor of 40 because [tex]\( 40 \div 2 = 20 \)[/tex].
3. Continue with the next integers:
Check if 3 is a factor of 40.
- 3 is not a factor of 40 because [tex]\( 40 \div 3 \)[/tex] leaves a remainder.
4. Check the next integer, 4:
- 4 is a factor of 40 because [tex]\( 40 \div 4 = 10 \)[/tex].
5. Check 5:
- 5 is a factor of 40 because [tex]\( 40 \div 5 = 8 \)[/tex].
6. Check 6:
- 6 is not a factor of 40 because [tex]\( 40 \div 6 \)[/tex] leaves a remainder.
7. Check 7:
- 7 is not a factor of 40 because [tex]\( 40 \div 7 \)[/tex] leaves a remainder.
8. Check 8:
- 8 is a factor of 40 because [tex]\( 40 \div 8 = 5 \)[/tex].
9. Check 9:
- 9 is not a factor of 40 because [tex]\( 40 \div 9 \)[/tex] leaves a remainder.
10. Check 10:
- 10 is a factor of 40 because [tex]\( 40 \div 10 = 4 \)[/tex].
11. Continue checking larger numbers until 40:
If a number divides 40 without a remainder, it is a factor. We continue this until we reach the number itself, 40.
- 20 is a factor of 40 because [tex]\( 40 \div 20 = 2 \)[/tex].
- 40 is a factor of 40 because [tex]\( 40 \div 40 = 1 \)[/tex].
After listing all such numbers, we collate them into a comprehensive list. Thus, the factors of 40 are:
[tex]\[ 1, 2, 4, 5, 8, 10, 20, 40 \][/tex]
