Divisors of 128

Divisors of a number are the whole numbers that can divide that number evenly without leaving a remainder. For example, if we say the number is 10, then 1, 2, 5, and 10 are its divisors because dividing 10 by any of these numbers results in a whole number. The purpose of this article is to explain what divisors are and how to find them, using the number 128 as our key example.

To understand divisors better, we need to look at the idea of division. Division involves three main parts: the dividend, the divisor, and the quotient. The dividend is the number we are dividing. The divisor is the number we are dividing by, and the quotient is the result we get from the division.

For example, if we take 128 as our dividend and divide it by 8 (the divisor), we set it up like this:
128 / 8 = 16

In this example:

• 128 is the dividend.
• 8 is the divisor.
• 16 is the quotient, which is a whole number.

Now, let’s go through a step-by-step guide on how to calculate the divisors of 128. We will divide 128 by every whole number starting from 1, all the way up to 128.

1. Start with the first integer, which is 1:

   • 128 / 1 = 128 (whole number)

2. Next, try 2:

   • 128 / 2 = 64 (whole number)

3. Now try 3:

   • 128 / 3 = 42.67 (not a whole number)

4. Now try 4:

   • 128 / 4 = 32 (whole number)

5. Next is 5:

   • 128 / 5 = 25.6 (not a whole number)

6. Then, we try 6:

   • 128 / 6 = 21.33 (not a whole number)

7. Now try 7:

   • 128 / 7 = 18.29 (not a whole number)

8. Now let’s check 8:

   • 128 / 8 = 16 (whole number)

9. Try 9:

   • 128 / 9 = 14.22 (not a whole number)
10. Finally, let’s try 10:
    • 128 / 10 = 12.8 (not a whole number)

Continuing this process up to 128, we find all the divisors. The whole number results that we discovered up to 10 are:

• 128 / 1 = 128
• 128 / 2 = 64
• 128 / 4 = 32
• 128 / 8 = 16

For brevity, we will not list all calculations beyond this point, and we will mention that similar checks can be performed with other integers up to 128.

In conclusion, the full list of all divisors of 128 includes:

1. 1
2. 2
3. 4
4. 8
5. 16
6. 32
7. 64
8. 128

So, the divisors of 128 are: 1, 2, 4, 8, 16, 32, 64, 128. Understanding divisors can help in many areas of math, including factors, multiples, and number theory.