Divisors of 126

When we talk about numbers, we often come across the term "divisor." Divisors are numbers that can divide another number without leaving a remainder. For instance, if we have the number 12, its divisors are the numbers that can perfectly fit into 12. Understanding divisors is essential in math as they help us break down numbers, simplify fractions, and work with ratios. In this article, we will focus on discovering the divisors of the number 126 and learn how to find them.

Let’s start with a simple explanation of division. Division is a way to find out how many times one number can fit into another. In division, we have three main terms: dividend, divisor, and quotient.

• The dividend is the number you want to divide.
• The divisor is the number you are dividing by.
• The quotient is the result you get from the division.

For example, let’s take one operation with the number 126:

• If we divide 126 by 1, we can see it like this:
  126 / 1 = 126. Here, 126 is the dividend, 1 is the divisor, and 126 is the quotient.

Now, let’s explore how to find the divisors of 126. We need to test which whole numbers can divide 126 without creating any fractions or remainders. To do this, we will divide 126 by every whole number starting from 1 and going all the way up to 126.

Step-by-step Guide:

1. Start with the number 1 and divide:

   • 126 / 1 = 126
   • Quotient is whole (divisor found).

2. Now, divide by 2:

   • 126 / 2 = 63
   • Quotient is whole (divisor found).

3. Next, divide by 3:

   • 126 / 3 = 42
   • Quotient is whole (divisor found).

4. Continue with 4:

   • 126 / 4 = 31.5
   • Quotient is not whole (not a divisor).

5. Try 5:

   • 126 / 5 = 25.2
   • Quotient is not whole (not a divisor).

6. Now divide by 6:

   • 126 / 6 = 21
   • Quotient is whole (divisor found).

7. Move on to 7:

   • 126 / 7 = 18
   • Quotient is whole (divisor found).

8. Test 8:

   • 126 / 8 = 15.75
   • Quotient is not whole (not a divisor).

9. Next, try 9:

   • 126 / 9 = 14
   • Quotient is whole (divisor found).
10. Finally for this section, test 10:
    • 126 / 10 = 12.6
    • Quotient is not whole (not a divisor).

We can see that the divisors we’ve found so far are: 1, 2, 3, 6, 7, and 9. We can keep dividing by numbers all the way up to 126, but for simplicity, let’s summarize our results with a few more calculations:

• 126 / 11 = 11.4545 (not a divisor).
• 126 / 12 = 10.5 (not a divisor).
• 126 / 14 = 9 (divisor found).
• 126 / 18 = 7 (already counted).
• 126 / 21 = 6 (already counted).
• 126 / 42 = 3 (already counted).
• 126 / 63 = 2 (already counted).
• 126 / 126 = 1 (already counted).

After going through all these divisions, we can summarize the complete list of divisors of 126.

Conclusion:
The complete set of divisors of 126 is:
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.

Divisors are a fundamental aspect of mathematics, helping us to simplify and understand numbers better. If you ever encounter a number, simply follow this method to find its divisors!