Divisors of 38

Divisors of a number are the integers that can divide that number without leaving a remainder. Understanding divisors helps us learn more about the properties of numbers and how they relate to each other. In this article, we will explore the concept of divisors using the example of the number 38, and we will go through the steps to find all the divisors of this number.

To begin with, let’s understand the concept of division. Division is when we split a number, called the dividend, into equal parts. The number we divide by is called the divisor, and the answer we get after performing the division is called the quotient. For example, in the division 38 / 2 = 19:

• 38 is the dividend (the number we are dividing).
• 2 is the divisor (the number we are dividing by).
• 19 is the quotient (the result of the division).

Now, let’s find the divisors of the number 38. To do this, we will divide the number 38 by every whole number starting from 1 and going up to 38. If the result of the division is a whole number, then that whole number is a divisor of 38.

Here’s a step-by-step guide to calculate the divisors of 38:

1. Start with 1 and go up to 38.
2. Divide 38 by each whole number and check if the quotient is a whole number (meaning there is no remainder).

Let’s perform these calculations:

1. 38 / 1 = 38 (whole number, so 1 is a divisor)
2. 38 / 2 = 19 (whole number, so 2 is a divisor)
3. 38 / 3 = 12.67 (not a whole number)
4. 38 / 4 = 9.5 (not a whole number)
5. 38 / 5 = 7.6 (not a whole number)
6. 38 / 6 = 6.33 (not a whole number)
7. 38 / 7 = 5.43 (not a whole number)
8. 38 / 8 = 4.75 (not a whole number)
9. 38 / 9 = 4.22 (not a whole number)
10. 38 / 10 = 3.8 (not a whole number)

Since we have checked all the numbers up to 10, and we know there will be more divisors for higher numbers, let’s check until we find all the divisors by continuing our calculations:

1. 38 / 11 = 3.45 (not a whole number)
2. 38 / 12 = 3.17 (not a whole number)
3. 38 / 13 = 2.92 (not a whole number)
4. 38 / 14 = 2.71 (not a whole number)
5. 38 / 15 = 2.53 (not a whole number)
6. 38 / 16 = 2.38 (not a whole number)
7. 38 / 17 = 2.24 (not a whole number)
8. 38 / 18 = 2.11 (not a whole number)
9. 38 / 19 = 2 (whole number, so 19 is a divisor)
10. 38 / 20 = 1.9 (not a whole number)
11. 38 / 21 = 1.81 (not a whole number)
12. 38 / 22 = 1.73 (not a whole number)
13. 38 / 23 = 1.65 (not a whole number)
14. 38 / 24 = 1.58 (not a whole number)
15. 38 / 25 = 1.52 (not a whole number)
16. 38 / 26 = 1.46 (not a whole number)
17. 38 / 27 = 1.41 (not a whole number)
18. 38 / 28 = 1.36 (not a whole number)
19. 38 / 29 = 1.31 (not a whole number)
20. 38 / 30 = 1.27 (not a whole number)
21. 38 / 31 = 1.23 (not a whole number)
22. 38 / 32 = 1.19 (not a whole number)
23. 38 / 33 = 1.15 (not a whole number)
24. 38 / 34 = 1.12 (not a whole number)
25. 38 / 35 = 1.09 (not a whole number)
26. 38 / 36 = 1.06 (not a whole number)
27. 38 / 37 = 1.03 (not a whole number)
28. 38 / 38 = 1 (whole number, so 38 is a divisor)

Now that we have performed all our calculations, let’s summarize the findings. The divisors of 38 are:

• 1
• 2
• 19
• 38

In conclusion, the complete list of divisors for the number 38 is: 1, 2, 19, 38. By understanding how to find divisors, you can discover more about the properties of numbers and how they interact with each other!