Divisors of 872

Divisors of a number are the integers that can divide that number without leaving a remainder. In simpler terms, divisors are the whole numbers that go into another whole number evenly. Understanding divisors helps us in many areas of math, such as simplifying fractions and finding greatest common factors. In this article, we’ll explore the divisors of the number 872.

To start, we need to understand the basic concept of division. When we divide, we use three terms:

1. Dividend: This is the number we are dividing. For example, in the division 872 / 1, 872 is the dividend.
2. Divisor: This is the number we are dividing by. In the same division example, 1 is the divisor.
3. Quotient: This is the result or answer from the division. In our example 872 / 1 = 872, the quotient is 872.

Now that we understand division, let’s explore how to find the divisors of 872.

To calculate the divisors of 872, we’ll divide 872 by every integer starting from 1 up to 872. We will look for numbers that divide evenly into 872, meaning the quotient will be a whole number with no remainder.

Here’s a step-by-step guide:

1. Start with 1 and divide 872 by 1.
   • 872 / 1 = 872 (whole number)
2. Next, divide by 2.
   • 872 / 2 = 436 (whole number)
3. Now, divide by 3.
   • 872 / 3 = 290.67 (not a whole number)
4. Then, divide by 4.
   • 872 / 4 = 218 (whole number)
5. Continue with 5.
   • 872 / 5 = 174.4 (not a whole number)
6. Next, divide by 6.
   • 872 / 6 = 145.33 (not a whole number)
7. Divide by 7.
   • 872 / 7 = 124.57 (not a whole number)
8. Then we try 8.
   • 872 / 8 = 109 (whole number)
9. Next is 9.
   • 872 / 9 = 96.89 (not a whole number)
10. Finally, divide by 10.
    • 872 / 10 = 87.2 (not a whole number)

Now let’s summarize the division calculations we’ve done:

• 872 / 1 = 872 (whole number)
• 872 / 2 = 436 (whole number)
• 872 / 3 = 290.67 (not a whole number)
• 872 / 4 = 218 (whole number)
• 872 / 5 = 174.4 (not a whole number)
• 872 / 6 = 145.33 (not a whole number)
• 872 / 7 = 124.57 (not a whole number)
• 872 / 8 = 109 (whole number)
• 872 / 9 = 96.89 (not a whole number)
• 872 / 10 = 87.2 (not a whole number)

We can see that the whole number quotients (divisors) we found are from dividing 872 by 1, 2, 4, and 8.

Continuing this process for all numbers up to 872 will give us all the divisors. However, for our summary, we will not continue beyond the initial divisors we calculated.

In conclusion, the divisors of 872 are:

1, 2, 4, 8, 109, 218, 436, 872

These numbers are the integers that can be multiplied together to give the number 872, and they can be useful in various mathematical applications, such as finding the greatest common divisor or simplifying fractions!