Divisors of 900

When we talk about divisors of a number, we are looking at the numbers that can divide that number without leaving a remainder. Understanding divisors is essential in mathematics because it helps us with operations like factoring, simplifying fractions, and working with whole numbers. In this article, we will explore the divisors of the number 900 and learn how to calculate them step by step.

To grasp the concept of divisors, we need to understand division first. In division, we break a number into equal parts. Here are the three important terms in division:

• Dividend: This is the number you want to divide.
• Divisor: This is the number you are dividing by.
• Quotient: This is the result of the division.

For example, if we have the division 900 / 1 = 900, here 900 is the dividend, 1 is the divisor, and 900 is the quotient. Let’s explore how to find the divisors of 900 by dividing it by integers from 1 to 900.

To find the divisors of 900, follow these steps:

1. Start with the number 1 and go up to 900.
2. For each integer (let’s call it the potential divisor), divide 900 by that integer.
3. Check if the result of the division is a whole number (meaning there is no remainder).

Let’s go through the calculations for the integers starting from 1 up to 20. We will list the divisions that give whole number results (divisors):

1. 900 / 1 = 900 (whole number)
2. 900 / 2 = 450 (whole number)
3. 900 / 3 = 300 (whole number)
4. 900 / 4 = 225 (whole number)
5. 900 / 5 = 180 (whole number)
6. 900 / 6 = 150 (whole number)
7. 900 / 9 = 100 (whole number)
8. 900 / 10 = 90 (whole number)
9. 900 / 12 = 75 (whole number)
10. 900 / 15 = 60 (whole number)

Continuing with integers higher than 15 will also yield divisors, but for brevity, we will state the process continues. The results show that there are many integers that can divide 900 without leaving a remainder.

Now, let’s summarize all the divisors of 900. To find all of them, we collect every integer that produced a whole number quotient:

• 1
• 2
• 3
• 4
• 5
• 6
• 9
• 10
• 12
• 15
• 18
• 20
• 25
• 30
• 36
• 45
• 60
• 75
• 90
• 100
• 150
• 180
• 225
• 300
• 450
• 900

In conclusion, the divisors of the number 900 are:
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900. Understanding divisors can help us with a variety of mathematical problems, providing a strong foundation for further study in the subject.