Divisors of 169

Divisors of a number are the whole numbers that can be multiplied together to yield that number. In other words, if you can divide a number evenly by another number, the second number is a divisor of the first. Understanding divisors helps in various areas of mathematics, including number theory and fractions. In this article, we’ll specifically look at the divisors of the number 169.

To understand how divisors work, we first need to grasp the concept of division. When you divide one number by another, you are breaking that number into equal parts. In division, the first number is called the dividend, the second number (the one you are dividing by) is called the divisor, and the result is called the quotient.

For example, let’s look at the equation 169 / 1 = 169:

• Here, 169 is the dividend.
• 1 is the divisor.
• 169 is also the quotient since dividing 169 by 1 gives us 169.

Now that we understand what divisors are and the basic terms of division, let’s go step-by-step to calculate the divisors of 169. To find all the divisors, we will divide 169 by every whole number starting from 1 and going up to 169.

1. Start with the number 1:

   • 169 / 1 = 169 (whole number, so 1 is a divisor)

2. Next, try 2:

   • 169 / 2 = 84.5 (not a whole number, so 2 is not a divisor)

3. Try 3:

   • 169 / 3 = 56.33 (not a whole number, so 3 is not a divisor)

4. Try 4:

   • 169 / 4 = 42.25 (not a whole number, so 4 is not a divisor)

5. Try 5:

   • 169 / 5 = 33.8 (not a whole number, so 5 is not a divisor)

6. Try 6:

   • 169 / 6 = 28.17 (not a whole number, so 6 is not a divisor)

7. Try 7:

   • 169 / 7 = 24.14 (not a whole number, so 7 is not a divisor)

8. Try 8:

   • 169 / 8 = 21.125 (not a whole number, so 8 is not a divisor)

9. Try 9:

   • 169 / 9 = 18.78 (not a whole number, so 9 is not a divisor)
10. Try 10:
    • 169 / 10 = 16.9 (not a whole number, so 10 is not a divisor)

Continuing in this manner, you can keep dividing until you reach 169. However, to make it easier, we can skip ahead by testing numbers that often could be divisors, especially those much less than 169.

After going through this process, we eventually find the divisors of 169. The division calculations leading to whole number quotients were as follows:

• 169 / 1 = 169 (1 is a divisor)
• 169 / 13 = 13 (13 is a divisor)
• 169 / 169 = 1 (169 is a divisor)

So, based on all our calculations, the complete list of divisors of 169 is:

• 1
• 13
• 169

In conclusion, the divisors of the number 169 are neatly listed as:
1, 13, 169