What is the sum of the divisors of 42?

To find the sum of the divisors of the number 42, we first need to identify all of its divisors. A divisor is any integer that can divide another integer without leaving a remainder. Let's break this down step by step.

Identifying the Divisors

The divisors of a number can be found by checking which numbers divide it evenly. For 42, we can start from 1 and go up to 42 itself. The divisors of 42 are:

• 1
• 2
• 3
• 6
• 7
• 14
• 21
• 42

Listing the Divisors

So, the complete list of divisors for 42 is: 1, 2, 3, 6, 7, 14, 21, and 42. Now, we can proceed to calculate the sum of these divisors.

Calculating the Sum

To find the sum, we simply add all the divisors together:

• 1 + 2 = 3
• 3 + 3 = 6
• 6 + 6 = 12
• 12 + 7 = 19
• 19 + 14 = 33
• 33 + 21 = 54
• 54 + 42 = 96

Final Calculation

When we add them all up, we find that the sum of the divisors of 42 is 96. This means that if you take all the numbers that can divide 42 without leaving a remainder and add them together, you will get 96.

Understanding the Importance

Finding the sum of divisors can be useful in various areas of mathematics, including number theory and when working with functions that involve divisors. It helps in understanding the properties of numbers and their relationships.

In summary, the sum of the divisors of 42 is 96, and we arrived at this by identifying all the divisors and then adding them together. This process not only gives us the answer but also reinforces our understanding of how divisors work.