Divisors of 144

Divisors of a number are the numbers that can perfectly divide that number without leaving any remainder. In simpler terms, if you can divide a number and get a whole number as a result, then that number is a divisor. Understanding divisors can help in many areas of math, such as simplifying fractions, finding factors, and even in solving problems related to divisibility. In this article, we will focus on the divisors of the number 144.

To start, let’s look at the concept of division, which is fundamental to understanding divisors. When you divide one number by another, you have three important terms:

1. Dividend: This is the number you want to divide. In our case, the dividend is 144.
2. Divisor: This is the number you divide by, which varies as we test different integers.
3. Quotient: This is the result of the division, which shows how many times the divisor fits into the dividend.

For example, in the division 144 / 12 = 12:

• 144 is the dividend.
• 12 is the divisor.
• 12 is the quotient.

Now, let’s learn how to calculate the divisors of 144. We will do this by checking every integer from 1 to 144 to see if it can divide 144 evenly. Here’s a step-by-step guide:

1. Start with the integer 1. Divide 144 by 1.
2. Next, take the integer 2 and divide 144 by 2.
3. Continue this process with each integer (3, 4, 5, etc.) up to 144.

Here are the results of our division calculations:

1. 144 / 1 = 144 (whole number)
2. 144 / 2 = 72 (whole number)
3. 144 / 3 = 48 (whole number)
4. 144 / 4 = 36 (whole number)
5. 144 / 5 = 28.8 (not a whole number)
6. 144 / 6 = 24 (whole number)
7. 144 / 7 = 20.57 (not a whole number)
8. 144 / 8 = 18 (whole number)
9. 144 / 9 = 16 (whole number)
10. 144 / 10 = 14.4 (not a whole number)
11. 144 / 11 = 13.09 (not a whole number)
12. 144 / 12 = 12 (whole number)

We can see that the divisors that produced whole numbers from dividing 144 by these integers are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 48, 72, and 144. For integers like 5, 7, 10, and 11, which provided non-whole number quotients, they are not divisors of 144.

In conclusion, the complete list of divisors of 144 is:

• 1
• 2
• 3
• 4
• 6
• 8
• 9
• 12
• 16
• 18
• 24
• 36
• 48
• 72
• 144

These numbers not only divide 144 evenly but also play an important role in many aspects of mathematics. Understanding divisors can pave the way for deeper mathematical exploration.