Divisors of 84

Numbers have special properties that help us understand how they relate to one another. One such property is called a "divisor." A divisor of a number is a whole number that can divide that number without leaving a remainder. In this article, we will explore the divisors of the number 84. We will learn how to find these divisors by using simple division and go step by step through the process.

To understand divisors, we first need to grasp the concept of division. Division is a way of splitting a number into equal parts. In division, we have three important terms:

1. Dividend: This is the number being divided. In our case, that is 84.
2. Divisor: This is the number by which we divide. For example, if we divide 84 by 2, then 2 is the divisor.
3. Quotient: This is the result of the division. It’s what you get when you divide the dividend by the divisor.

Let’s illustrate this with the division of 84 by 2:

• 84 / 2 = 42
  Here, 84 is the dividend, 2 is the divisor, and 42 is the quotient.

Now, let’s find the divisors of 84. We will do this by dividing 84 by every integer starting from 1 up to 84 itself. If the result (the quotient) is a whole number, then that integer is a divisor of 84.

We will start dividing 84 by each integer from 1 to 10:

1. 84 / 1 = 84 (Whole number, so 1 is a divisor)
2. 84 / 2 = 42 (Whole number, so 2 is a divisor)
3. 84 / 3 = 28 (Whole number, so 3 is a divisor)
4. 84 / 4 = 21 (Whole number, so 4 is a divisor)
5. 84 / 5 = 16.8 (Not a whole number, so 5 is not a divisor)
6. 84 / 6 = 14 (Whole number, so 6 is a divisor)
7. 84 / 7 = 12 (Whole number, so 7 is a divisor)
8. 84 / 8 = 10.5 (Not a whole number, so 8 is not a divisor)
9. 84 / 9 = 9.33 (Not a whole number, so 9 is not a divisor)
10. 84 / 10 = 8.4 (Not a whole number, so 10 is not a divisor)

We can continue this process for integers up to 84. The goal is to identify all the numbers that divide evenly into 84 (those that give a whole number as a result).

To summarize our findings up to the number 10, we have identified the following divisors of 84:

1. 1
2. 2
3. 3
4. 4
5. 6
6. 7

Continuing this process gives us additional divisors. When fully calculated, the complete list of divisors for 84 is:

• 1
• 2
• 3
• 4
• 6
• 7
• 12
• 14
• 21
• 28
• 42
• 84

To conclude, we have explored the concept of divisors through the number 84. We learned that divisors are numbers that fit evenly into another number, providing a whole quotient. The complete set of divisors for 84 is 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. Understanding divisors helps us appreciate the relationships between numbers and their properties!