Divisors of 105

Divisors of a number are the whole numbers that can be divided evenly into that number, meaning when you divide, there is no remainder. For example, if you have a number like 12, the divisors would be the numbers you can divide into 12 without leaving anything left over. In this article, we will explore the concept of divisors, how to find them, and specifically look at the divisors of the number 105.

To understand divisors, we first need to talk about division. Division is a way of breaking a number into equal parts. In division, we have three important terms:

• Dividend: This is the number we are dividing. In this case, for 105, the dividend is 105.
• Divisor: This is the number we are dividing by. For each step we will test the divisors from 1 to 105.
• Quotient: This is the result of the division. It tells us how many times the divisor fits into the dividend.

For example, if we want to divide 105 by 1, we write it like this:
105 / 1 = 105
Here, 105 is the dividend, 1 is the divisor, and 105 is also the quotient. Now, let’s explore how to find the divisors of 105 step-by-step.

To calculate the divisors of 105, we will divide 105 by every whole number starting from 1 up to 105. If the result of the division (the quotient) is a whole number, then that number is a divisor of 105. Let’s do this step by step:

1. 105 / 1 = 105 (whole number, so 1 is a divisor)
2. 105 / 2 = 52.5 (not a whole number)
3. 105 / 3 = 35 (whole number, so 3 is a divisor)
4. 105 / 4 = 26.25 (not a whole number)
5. 105 / 5 = 21 (whole number, so 5 is a divisor)
6. 105 / 6 = 17.5 (not a whole number)
7. 105 / 7 = 15 (whole number, so 7 is a divisor)
8. 105 / 8 = 13.125 (not a whole number)
9. 105 / 9 = 11.666… (not a whole number)
10. 105 / 10 = 10.5 (not a whole number)

Continuing this process would lead us to other divisors, such as 15, 21, 35, and 105. For simplicity, we can note that there are other whole numbers to check beyond 10.

Here’s a quick list of some results from our calculations where the division gives whole numbers:

• 105 / 1 = 105
• 105 / 3 = 35
• 105 / 5 = 21
• 105 / 7 = 15
• 105 / 15 = 7
• 105 / 21 = 5
• 105 / 35 = 3
• 105 / 105 = 1

Now, let’s summarize and list all the divisors of 105 clearly:

Divisors of 105:

1. 1
2. 3
3. 5
4. 7
5. 15
6. 21
7. 35
8. 105

In conclusion, the divisors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105. Understanding divisors is important in mathematics because it helps us break down numbers and understand their properties better.