Divisors of 680

Divisors are numbers that can evenly divide another number without leaving a remainder. Understanding divisors can help us in various areas of math, such as solving equations, factoring numbers, and understanding properties of numbers. This article will explain what divisors are and how to find them, specifically using the number 680 as our example.

What is Division?

Division is a mathematical operation where we split a number into equal parts. In this operation, we have three important terms:

• Dividend: This is the number we want to divide. For example, in the case of 680, it is the dividend.
• Divisor: This is the number we are dividing by. For instance, if we divide 680 by 2, then 2 is the divisor.
• Quotient: This is the result of the division. If we divide 680 by 2, the quotient is 340.

So, we can write it like this:
680 / 2 = 340

How to Calculate the Divisors of 680

To find the divisors of 680, we will divide it by every whole number starting from 1 up to 680. Whenever the result of the division (the quotient) is a whole number, the divisor is a divisor of 680.

Let’s go step-by-step through the process:

1. Start with the integer 1 and divide 680 by it.
2. Continue this process up to the number 680.

Division Calculations for 680

Here are the division calculations showing which numbers divide evenly into 680:

1. 680 / 1 = 680
   (1 is a divisor)

2. 680 / 2 = 340
   (2 is a divisor)

3. 680 / 3 = 226.67
   (3 is not a divisor)

4. 680 / 4 = 170
   (4 is a divisor)

5. 680 / 5 = 136
   (5 is a divisor)

6. 680 / 6 = 113.33
   (6 is not a divisor)

7. 680 / 7 = 97.14
   (7 is not a divisor)

8. 680 / 8 = 85
   (8 is a divisor)

9. 680 / 9 = 75.56
   (9 is not a divisor)

10. 680 / 10 = 68
    (10 is a divisor)

… etc.

We can see that the divisors of 680 are 1, 2, 4, 5, 8, and 10 up to this point where whole numbers resulted as the quotient.

Conclusion

After calculating the divisors of 680, we find that the complete list of divisors includes:

1, 2, 4, 5, 8, 10, 17, 20, 34, 68, 85, 136, 170, 340, and 680.

This means that these numbers can divide 680 evenly without leaving any remainder. Understanding how to find divisors is a key math skill that helps in many other areas of study!