When we talk about the divisors of a number, we are referring to the numbers that can be divided into it evenly, meaning they leave no remainder. Understanding divisors helps us break down numbers, find relationships between them, and perform various mathematical operations. This article will explain what divisors are using the number 728 as an example, so you can see how to find them clearly and simply.
To understand divisors, we need to look at the concept of division. In division, we have three important terms: the dividend, the divisor, and the quotient. The dividend is the number we want to divide, the divisor is the number we are dividing by, and the quotient is the result we get from the division.
For example, in the equation 728 / 1 = 728:
– 728 is the dividend
– 1 is the divisor
– 728 is the quotient
Now that we understand these terms, let’s look at how to find the divisors of the number 728. To do this, you will divide 728 by every whole number starting from 1 up to 728. If the result of the division leaves no remainder (which means it is a whole number), then that number is a divisor of 728.
Let’s go through the steps:
1. Start with 1 and divide 728.
2. Then go to 2 and divide 728.
3. Continue this process until you reach 728.
Here are the division calculations for the different numbers. We will only show examples up to 10.
1. 728 / 1 = 728 (whole number, so 1 is a divisor)
2. 728 / 2 = 364 (whole number, so 2 is a divisor)
3. 728 / 3 = 242.67 (not a whole number, so 3 is NOT a divisor)
4. 728 / 4 = 182 (whole number, so 4 is a divisor)
5. 728 / 5 = 145.6 (not a whole number, so 5 is NOT a divisor)
6. 728 / 6 = 121.33 (not a whole number, so 6 is NOT a divisor)
7. 728 / 7 = 104 (whole number, so 7 is a divisor)
8. 728 / 8 = 91 (whole number, so 8 is a divisor)
9. 728 / 9 = 80.89 (not a whole number, so 9 is NOT a divisor)
10. 728 / 10 = 72.8 (not a whole number, so 10 is NOT a divisor)
11. 728 / 11 = 66.18 (not a whole number, so 11 is NOT a divisor)
12. 728 / 12 = 60.67 (not a whole number, so 12 is NOT a divisor)
13. 728 / 13 = 56.77 (not a whole number, so 13 is NOT a divisor)
14. 728 / 14 = 52 (whole number, so 14 is a divisor)
15. 728 / 15 = 48.53 (not a whole number, so 15 is NOT a divisor)
16. 728 / 16 = 45.5 (not a whole number, so 16 is NOT a divisor)
17. 728 / 17 = 42.82 (not a whole number, so 17 is NOT a divisor)
18. 728 / 18 = 40.44 (not a whole number, so 18 is NOT a divisor)
19. 728 / 19 = 38.37 (not a whole number, so 19 is NOT a divisor)
20. 728 / 20 = 36.4 (not a whole number, so 20 is NOT a divisor)
21. 728 / 21 = 34.67 (not a whole number, so 21 is NOT a divisor)
Now that we have gone through the calculations, let’s list all the divisors that we found:
The divisors of 728 are:
1, 2, 4, 7, 8, 14, 182, 364, and 728.
In conclusion, the divisors of the number 728 include all the numbers that can divide it evenly: 1, 2, 4, 7, 8, 14, 182, 364, and 728. Understanding how to find and list these divisors can be beneficial in various areas of math, including factoring, finding common multiples, and solving equations.