Divisors of 156

When we talk about the divisors of a number, we are referring to the integers that can divide that number without leaving a remainder. Understanding divisors is important in mathematics because they help us in various fields, including fractions, factors, and number theory. In this article, we’ll explore the divisors of the number 156.

To understand divisors, we first need to know about division. Division is a way to split a number into equal parts. In a division equation, we have three important terms:

• Dividend: The number that we want to divide. In our example, this is 156.
• Divisor: The number by which we divide the dividend. This will be each integer we test against 156.
• Quotient: The result we get from the division. If there’s no remainder, then it’s a whole number.

Let’s look at an example with the number 156. If we divide 156 by 1, we would write it like this:

156 / 1 = 156

In this case, 156 is the dividend, 1 is the divisor, and 156 is also the quotient.

Now, let’s find the divisors of 156. To do this, we divide 156 by every integer starting from 1 up to 156.

Here is the step-by-step guide to calculate the divisors of 156:

1. Start with the number 1 and go up to 156.
2. For each integer, divide 156 by it.
3. If the division results in a whole number (meaning there’s no remainder), then that integer is a divisor of 156.

Now, let’s do the calculations:

1. 156 / 1 = 156 (whole number)
2. 156 / 2 = 78 (whole number)
3. 156 / 3 = 52 (whole number)
4. 156 / 4 = 39 (whole number)
5. 156 / 5 = 31.2 (not a whole number)
6. 156 / 6 = 26 (whole number)
7. 156 / 7 = 22.2857 (not a whole number)
8. 156 / 8 = 19.5 (not a whole number)
9. 156 / 9 = 17.3333 (not a whole number)
10. 156 / 10 = 15.6 (not a whole number)
11. 156 / 12 = 13 (whole number)
12. 156 / 13 = 12 (whole number)
13. 156 / 14 = 11.1429 (not a whole number)
14. 156 / 15 = 10.4 (not a whole number)
15. 156 / 16 = 9.75 (not a whole number)
16. 156 / 17 = 9.1765 (not a whole number)
17. 156 / 18 = 8.6667 (not a whole number)
18. 156 / 19 = 8.2105 (not a whole number)
19. 156 / 20 = 7.8 (not a whole number)
20. 156 / 26 = 6 (whole number)
21. 156 / 39 = 4 (whole number)
22. 156 / 52 = 3 (whole number)
23. 156 / 78 = 2 (whole number)
24. 156 / 156 = 1 (whole number)

As we can see, the calculations show which numbers produce whole-number results. The successful divisions are:

• 156 / 1 = 156
• 156 / 2 = 78
• 156 / 3 = 52
• 156 / 4 = 39
• 156 / 6 = 26
• 156 / 12 = 13
• 156 / 13 = 12
• 156 / 26 = 6
• 156 / 39 = 4
• 156 / 52 = 3
• 156 / 78 = 2
• 156 / 156 = 1

Now, let’s list all the divisors of 156 in a neat format:

Divisors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.

In conclusion, the process of finding the divisors of a number involves testing each integer to see if it divides evenly into the number. The divisors help us understand the properties of the number better, and in the case of 156, we found a total of 12 divisors.