Let's solve the question step-by-step to find the divisors of 60:
1. Identify the Number: The number in question is 60. We need to find all the positive integers that divide 60 without leaving a remainder.
2. Begin with the Smallest Divisor:
- The smallest positive integer is 1. Since every number is divisible by 1, 1 is a divisor of 60.
3. Check Consecutive Numbers:
- Next is 2. The number 60 is even, so it is divisible by 2.
- Then 3. Summing the digits of 60 (i.e., 6 + 0 = 6) gives a result divisible by 3, so 3 is a divisor.
- After 3, check 4. Divide 60 by 4, which results in 15. Thus, 4 is a divisor.
- Next is 5. Since 60 ends in a 0, it is divisible by 5.
- Then come 6, 10, 12, 15, 20, 30, and finally 60 itself. Each of these numbers divides 60 exactly.
4. List All Divisors:
- From the previous steps, we determine that the list of divisors is:
[tex]\[
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
\][/tex]
5. Final Answer:
- Therefore, the divisors of 60 are:
[tex]\[
\boxed{1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}.
\][/tex]
This detailed step-by-step process ensures that we've correctly identified all the numbers that evenly divide 60.
