Divisors of 86

Divisors of a number are the numbers that can be evenly divided into that number without leaving a remainder. Understanding divisors helps us in various areas of mathematics, including simplification of fractions, finding common factors, and understanding the properties of numbers. In this article, we will explore the divisors of the number 86.

To understand divisors, we need to look at division. When we divide, we use three main terms:

• Dividend: The number we want to divide (in our case, 86).
• Divisor: The number we are dividing by (for example, 2).
• Quotient: The result we get from the division (how many times the divisor fits into the dividend).

In a division formula, it looks like this:
86 / 2 = 43

Here, 86 is the dividend, 2 is the divisor, and 43 is the quotient.

Now let’s find the divisors of 86. To do this, we will divide 86 by every integer from 1 up to 86 itself. A divisor is a number that divides evenly into 86, meaning the quotient must be a whole number (no decimals or fractions).

Let’s go step-by-step:

1. Start with the number 1:
   86 / 1 = 86
   (whole number, so 1 is a divisor)

2. Next, try 2:
   86 / 2 = 43
   (whole number, so 2 is a divisor)

3. Now, check 3:
   86 / 3 = 28.67
   (not a whole number, so 3 is not a divisor)

4. Try 4:
   86 / 4 = 21.5
   (not a whole number, so 4 is not a divisor)

5. Next up is 5:
   86 / 5 = 17.2
   (not a whole number, so 5 is not a divisor)

6. Check 6:
   86 / 6 = 14.33
   (not a whole number, so 6 is not a divisor)

7. Now for 7:
   86 / 7 = 12.29
   (not a whole number, so 7 is not a divisor)

8. Try 8:
   86 / 8 = 10.75
   (not a whole number, so 8 is not a divisor)

9. Check 9:
   86 / 9 = 9.56
   (not a whole number, so 9 is not a divisor)

10. Now, check 10:
    86 / 10 = 8.6
    (not a whole number, so 10 is not a divisor)

11. Next is 11:
    86 / 11 = 7.82
    (not a whole number, so 11 is not a divisor)

12. Try 12:
    86 / 12 = 7.17
    (not a whole number, so 12 is not a divisor)

13. Next, check 13:
    86 / 13 = 6.62
    (not a whole number, so 13 is not a divisor)

14. Check 14:
    86 / 14 = 6.14
    (not a whole number, so 14 is not a divisor)

15. Now for 15:
    86 / 15 = 5.73
    (not a whole number, so 15 is not a divisor)

16. Try 16:
    86 / 16 = 5.375
    (not a whole number, so 16 is not a divisor)

17. Checking 17:
    86 / 17 = 5.06
    (not a whole number, so 17 is not a divisor)

18. Finally, check 86:
    86 / 86 = 1
    (whole number, so 86 is a divisor)

From our calculations, the divisors of 86 that produced whole numbers are 1, 2, 43, and 86.

In conclusion, the complete list of divisors of 86 is:
1, 2, 43, and 86.