When we talk about the divisors of a number, we are referring to the numbers that can divide that number evenly, which means there is no remainder left over. The purpose of this article is to explain what divisors are and how to find them, using the example of the number 273.
To understand divisors better, we need to look at the concept of division. Division is the process of splitting a number into equal parts. In division, we have three key terms:
- Dividend: the number being divided (for example, 273);
- Divisor: the number we are dividing by (for example, 1, 2, 3, etc.);
- Quotient: the result of the division.
So, if we divide 273 by 1, we can write it like this:
273 / 1 = 273
In this case, 273 is the dividend, 1 is the divisor, and 273 is the quotient.
Now, let’s find the divisors of 273 by dividing this number by every integer from 1 up to 273. We will check which divisions produce a whole number (meaning there is no remainder).
Here’s a step-by-step guide:
- Start with the number 1 and divide 273 by it.
- Move to the next integer (2) and divide 273 by it.
- Continue this process until you reach 273.
Here are the calculations:
- 273 / 1 = 273 (whole number)
- 273 / 2 = 136.5 (not a whole number)
- 273 / 3 = 91 (whole number)
- 273 / 4 = 68.25 (not a whole number)
- 273 / 5 = 54.6 (not a whole number)
- 273 / 6 = 45.5 (not a whole number)
- 273 / 7 = 39 (whole number)
- 273 / 8 = 34.125 (not a whole number)
- 273 / 9 = 30.333… (not a whole number)
- 273 / 10 = 27.3 (not a whole number)
- 273 / 11 = 24.8181… (not a whole number)
- 273 / 12 = 22.75 (not a whole number)
- 273 / 13 = 21 (whole number)
- 273 / 14 = 19.5 (not a whole number)
- 273 / 15 = 18.2 (not a whole number)
- 273 / 16 = 17.0625 (not a whole number)
- 273 / 17 = 16.0588… (not a whole number)
- 273 / 18 = 15.1666… (not a whole number)
- 273 / 19 = 14.3684… (not a whole number)
- 273 / 20 = 13.65 (not a whole number)
- 273 / 21 = 13 (whole number)
- 273 / 22 = 12.4090… (not a whole number)
- 273 / 23 = 11.8695… (not a whole number)
- 273 / 24 = 11.375 (not a whole number)
- 273 / 25 = 10.92 (not a whole number)
- 273 / 26 = 10.5 (not a whole number)
- 273 / 27 = 10.1111… (not a whole number)
- 273 / 28 = 9.75 (not a whole number)
- 273 / 29 = 9.41379… (not a whole number)
- 273 / 30 = 9.1 (not a whole number)
- 273 / 31 = 8.80645… (not a whole number)
- 273 / 32 = 8.53125 (not a whole number)
- 273 / 33 = 8.2727… (not a whole number)
- 273 / 34 = 8.0294… (not a whole number)
- 273 / 35 = 7.8 (not a whole number)
- 273 / 36 = 7.5833… (not a whole number)
- 273 / 37 = 7.3704… (not a whole number)
- 273 / 38 = 7.1842… (not a whole number)
- 273 / 39 = 7 (whole number)
- and so on…
Based on the calculations above, the whole number quotients we found where the division resulted in a whole number (no remainders) are:
- 1
- 3
- 7
- 13
- 21
- 39
- 91
- 273
In conclusion, the complete list of divisors for the number 273 is:
1, 3, 7, 13, 21, 39, 91, 273.
These are all the numbers that can be multiplied by another whole number to give 273 with no remainder!