Divisors of 684

Divisors of a number are the integers that can divide that number without leaving a remainder. Understanding divisors is important in various areas of mathematics, including number theory and fractions. This article will take a closer look at the divisors of the number 684.

To understand divisors, we first need to know about division. In a division operation, we have three key terms:

• Dividend: This is the number we want to divide. For example, in the equation 684 / 1 = 684, 684 is the dividend.
• Divisor: This is the number we are dividing by. In the same example, 1 is the divisor.
• Quotient: This is the result of the division. In our example, 684 / 1 = 684, the quotient is 684.

Now, let’s find the divisors of 684 by dividing the number by every integer starting from 1 up to 684 itself.

To calculate the divisors of 684, we will systematically divide 684 by each integer from 1 to 20. If the division results in a whole number (no remainder), then that integer is a divisor of 684.

Here’s how the calculations work out for some examples:

1. 684 / 1 = 684 (whole number)
2. 684 / 2 = 342 (whole number)
3. 684 / 3 = 228 (whole number)
4. 684 / 4 = 171 (whole number)
5. 684 / 5 = 136.8 (not a whole number)
6. 684 / 6 = 114 (whole number)
7. 684 / 7 = 97.7142857 (not a whole number)
8. 684 / 8 = 85.5 (not a whole number)
9. 684 / 9 = 76 (whole number)
10. 684 / 10 = 68.4 (not a whole number)
11. 684 / 11 = 62.5454545 (not a whole number)
12. 684 / 12 = 57 (whole number)
13. 684 / 13 = 52.6153846 (not a whole number)
14. 684 / 14 = 48.8571428 (not a whole number)
15. 684 / 15 = 45.6 (not a whole number)
16. 684 / 16 = 42.75 (not a whole number)
17. 684 / 17 = 40.2352941 (not a whole number)
18. 684 / 18 = 38 (whole number)
19. 684 / 19 = 36 (whole number)
20. 684 / 20 = 34.2 (not a whole number)

From our divisions, the integers that produced whole numbers are:

• 1
• 2
• 3
• 4
• 6
• 9
• 12
• 18
• 19
• 342 (this needs to be checked with larger numbers, we only need to find up to half of 684, which is 342)

For 684, the complete list of divisors includes both the factors we calculated and their complements. For example, since 1 is a divisor, 684 / 1 gives us 684, and so on.

In conclusion, the complete list of all the divisors of 684 is:

1, 2, 3, 4, 6, 9, 12, 18, 19, 34, 57, 68, 76, 114, 171, 228, 342, 684.

Understanding divisors helps us break down numbers into smaller parts and is foundational for many mathematical concepts.