Divisors of a number are the numbers that can divide that number without leaving a remainder. Understanding divisors helps in various areas of math, such as simplifying fractions, finding common factors, and solving problems in number theory. In this article, we’ll explore the divisors of the number 975, providing simple explanations and calculations along the way.
To grasp the concept of divisors, we first need to understand division. Let’s break down the terms involved:
- Dividend: This is the number you want to divide. In our case, that’s 975.
- Divisor: This is the number you are dividing by. This will be each integer we test to find divisors of 975.
- Quotient: This is the result you get after dividing the dividend by the divisor.
For example, let’s look at the division 975 / 5. Here, 975 is the dividend, 5 is the divisor, and if we calculate it, we get:
975 / 5 = 195
So, here, 195 is the quotient.
Now, let’s find the divisors of 975 by dividing it by every whole number starting from 1 up to 975. We will only check numbers from 1 to 10 for our step-by-step guide, as that will give us a good idea of how this works.
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Start with 1:
975 / 1 = 975 (whole number, so 1 is a divisor) -
Next is 2:
975 / 2 = 487.5 (not a whole number, so 2 is not a divisor) -
Next is 3:
975 / 3 = 325 (whole number, so 3 is a divisor) -
Next is 4:
975 / 4 = 243.75 (not a whole number, so 4 is not a divisor) -
Next is 5:
975 / 5 = 195 (whole number, so 5 is a divisor) -
Next is 6:
975 / 6 = 162.5 (not a whole number, so 6 is not a divisor) -
Next is 7:
975 / 7 = 139.2857 (not a whole number, so 7 is not a divisor) -
Next is 8:
975 / 8 = 121.875 (not a whole number, so 8 is not a divisor) -
Next is 9:
975 / 9 = 108.3333 (not a whole number, so 9 is not a divisor) - Next is 10:
975 / 10 = 97.5 (not a whole number, so 10 is not a divisor)
From these calculations, the whole numbers we found that can divide 975 without leaving a remainder (the divisors) are 1, 3, and 5.
In conclusion, after checking all numbers from 1 to 10, the complete list of divisors of 975 is:
- 1
- 3
- 5
- 15 (since 975 / 15 = 65)
- 25 (since 975 / 25 = 39)
- 39 (since 975 / 39 = 25)
- 65 (since 975 / 65 = 15)
- 195 (since 975 / 195 = 5)
- 325 (since 975 / 325 = 3)
- 975 (since 975 / 975 = 1)
So, all the divisors of 975 are 1, 3, 5, 15, 25, 39, 65, 195, 325, and 975. Understanding how to find and identify divisors is a valuable skill in various fields of mathematics!