Divisors of 35

When we talk about divisors of a number, we are referring to the integers that can divide that number evenly, without leaving a remainder. In simpler terms, if you can divide a number by another number and get a whole number as the answer, then that second number is a divisor of the first. This article will help you understand what divisors are and how to find them, using the number 35 as our example.

To understand divisors better, let’s first look at the idea of division. When we divide a number, we have three key terms:

1. Dividend: This is the number we are dividing. In our case with 35, 35 will be the dividend.
2. Divisor: This is the number we are using to divide the dividend. We will check each number from 1 to 35 to see if it is a divisor of 35.
3. Quotient: This is the result we get after doing the division.

For example, if we want to divide 35 by 5, we write it like this:

35 / 5 = 7

In this case, 35 is the dividend, 5 is the divisor, and 7 is the quotient. Since 7 is a whole number, we can say that 5 is a divisor of 35.

Now let’s find out the divisors of 35. We will divide 35 by every integer from 1 up to 35. We will check if the result gives us a whole number.

Step-by-Step Calculation of Divisors of 35

1. Start with 1:

   • 35 / 1 = 35 (whole number; 1 is a divisor)

2. Next, try 2:

   • 35 / 2 = 17.5 (not a whole number; 2 is not a divisor)

3. Try 3:

   • 35 / 3 = 11.67 (not a whole number; 3 is not a divisor)

4. Try 4:

   • 35 / 4 = 8.75 (not a whole number; 4 is not a divisor)

5. Try 5:

   • 35 / 5 = 7 (whole number; 5 is a divisor)

6. Try 6:

   • 35 / 6 = 5.83 (not a whole number; 6 is not a divisor)

7. Try 7:

   • 35 / 7 = 5 (whole number; 7 is a divisor)

8. Try 8:

   • 35 / 8 = 4.375 (not a whole number; 8 is not a divisor)

9. Try 9:

   • 35 / 9 = 3.89 (not a whole number; 9 is not a divisor)

10. Try 10:

    • 35 / 10 = 3.5 (not a whole number; 10 is not a divisor)

11. Try 11:

    • 35 / 11 = 3.18 (not a whole number; 11 is not a divisor)

12. Try 12:

    • 35 / 12 = 2.92 (not a whole number; 12 is not a divisor)

13. Try 13:

    • 35 / 13 = 2.69 (not a whole number; 13 is not a divisor)

14. Try 14:

    • 35 / 14 = 2.5 (not a whole number; 14 is not a divisor)

15. Try 15:

    • 35 / 15 = 2.33 (not a whole number; 15 is not a divisor)

16. Try 16:

    • 35 / 16 = 2.19 (not a whole number; 16 is not a divisor)

17. Try 17:

    • 35 / 17 = 2.06 (not a whole number; 17 is not a divisor)

18. Try 18:

    • 35 / 18 = 1.94 (not a whole number; 18 is not a divisor)

19. Try 19:

    • 35 / 19 = 1.84 (not a whole number; 19 is not a divisor)

20. Try 20:

    • 35 / 20 = 1.75 (not a whole number; 20 is not a divisor)

21. Try 21:

    • 35 / 21 = 1.67 (not a whole number; 21 is not a divisor)

22. Try 22:

    • 35 / 22 = 1.59 (not a whole number; 22 is not a divisor)

23. Try 23:

    • 35 / 23 = 1.52 (not a whole number; 23 is not a divisor)

24. Try 24:

    • 35 / 24 = 1.46 (not a whole number; 24 is not a divisor)

25. Try 25:

    • 35 / 25 = 1.4 (not a whole number; 25 is not a divisor)

26. Try 26:

    • 35 / 26 = 1.35 (not a whole number; 26 is not a divisor)

27. Try 27:

    • 35 / 27 = 1.3 (not a whole number; 27 is not a divisor)

28. Try 28:

    • 35 / 28 = 1.25 (not a whole number; 28 is not a divisor)

29. Try 29:

    • 35 / 29 = 1.21 (not a whole number; 29 is not a divisor)

30. Try 30:

    • 35 / 30 = 1.17 (not a whole number; 30 is not a divisor)

31. Try 31:

    • 35 / 31 = 1.13 (not a whole number; 31 is not a divisor)

32. Try 32:

    • 35 / 32 = 1.09 (not a whole number; 32 is not a divisor)

33. Try 33:

    • 35 / 33 = 1.06 (not a whole number; 33 is not a divisor)

34. Try 34:

    • 35 / 34 = 1.03 (not a whole number; 34 is not a divisor)
35. Finally, try 35:
    • 35 / 35 = 1 (whole number; 35 is a divisor)

Summary of Divisors of 35

After checking all the numbers, we find that the divisors of 35 are:

• 1
• 5
• 7
• 35

So, the complete list of divisors of 35 is: 1, 5, 7, 35.