Divisors of a number are the integers that can divide that number without leaving any remainder. In simpler terms, if you can divide a number by another number and get a whole number as the result, then that second number is called a divisor of the first number. In this article, we will explore the concept of divisors, how to find them, and specifically look at the divisors of the number 78.
To understand divisors, it’s essential to first grasp the concept of division. Division is the process of splitting a number into equal parts. The number you want to divide is called the “dividend.” The number you are dividing by is called the “divisor,” and the result of the division is called the “quotient.” Here’s an example:
If we have the equation 78 / 2 = 39:
– 78 is the dividend.
– 2 is the divisor.
– 39 is the quotient.
This means that when we divide 78 by 2, we get 39, which is a whole number. Therefore, 2 is a divisor of 78.
Now, let’s learn how to calculate the divisors of the number 78 step by step. We will divide 78 by every integer starting from 1 up to 78. This way, we can find out which of these integers are divisors of 78.
1. Start with the first integer, which is 1.
– 78 / 1 = 78 (whole number, so 1 is a divisor)
2. Next, try 2.
– 78 / 2 = 39 (whole number, so 2 is a divisor)
3. Next, try 3.
– 78 / 3 = 26 (whole number, so 3 is a divisor)
4. Next, try 4.
– 78 / 4 = 19.5 (not a whole number, so 4 is not a divisor)
5. Next, try 5.
– 78 / 5 = 15.6 (not a whole number, so 5 is not a divisor)
6. Next, try 6.
– 78 / 6 = 13 (whole number, so 6 is a divisor)
7. Next, try 7.
– 78 / 7 = 11.14 (not a whole number, so 7 is not a divisor)
8. Next, try 8.
– 78 / 8 = 9.75 (not a whole number, so 8 is not a divisor)
9. Next, try 9.
– 78 / 9 = 8.67 (not a whole number, so 9 is not a divisor)
10. Next, try 10.
– 78 / 10 = 7.8 (not a whole number, so 10 is not a divisor)
We can continue this process all the way up to 78, but we can summarize the findings.
Here are the results of the division calculations for the divisors of 78:
– 78 / 1 = 78 (1 is a divisor)
– 78 / 2 = 39 (2 is a divisor)
– 78 / 3 = 26 (3 is a divisor)
– 78 / 6 = 13 (6 is a divisor)
The process continues with 12, 13, 26, 39, and finally, 78 itself. Some divisors produce whole numbers; others do not. The divisors of 78 that we found that yield whole numbers are:
1, 2, 3, 6, 13, 26, 39, 78
In conclusion, the complete list of all divisors of 78 is:
– 1
– 2
– 3
– 6
– 13
– 26
– 39
– 78
These numbers are all the divisors of 78, meaning they can divide 78 evenly without any remainder. Understanding divisors can be quite helpful in various areas of mathematics, including factoring and simplifying fractions!