Divisors of 426

Divisors are numbers that can perfectly divide another number without leaving a remainder. Understanding divisors is important in mathematics because they help us explore the relationships between numbers, find factors, and simplify fractions. In this article, we will look closely at the divisors of the number 426.

To understand divisors better, we need to learn about division. When we divide, we use three main terms:

1. Dividend: This is the number we want to divide. In our example, the dividend is 426.
2. Divisor: This is the number we are dividing by. We will use integers starting from 1 and going up to 426.
3. Quotient: This is the result we get from the division. If the division is exact, meaning there’s no remainder, the quotient will be a whole number.

For example, if we divide 426 by 2, we express it like this:
426 / 2 = 213
In this case, 426 is the dividend, 2 is the divisor, and 213 is the quotient.

Now, let’s find out the divisors of 426 by checking every integer from 1 up to 426. We will divide 426 by each integer and see if the quotient is a whole number. If it is, that integer is a divisor of 426.

Here’s how we will proceed:

1. Start at 1 and go up to 426.
2. For each integer ( n ) (where ( n ) is 1, 2, 3, and so on), divide 426 by ( n ).
3. If 426 / ( n ) results in a whole number, then ( n ) is a divisor.

Let’s calculate and see the results for the first 10 integers:

1. 426 / 1 = 426 (whole number, so 1 is a divisor)
2. 426 / 2 = 213 (whole number, so 2 is a divisor)
3. 426 / 3 = 142 (whole number, so 3 is a divisor)
4. 426 / 4 = 106.5 (not a whole number)
5. 426 / 5 = 85.2 (not a whole number)
6. 426 / 6 = 71 (whole number, so 6 is a divisor)
7. 426 / 7 = 60.857 (not a whole number)
8. 426 / 8 = 53.25 (not a whole number)
9. 426 / 9 = 47.333 (not a whole number)
10. 426 / 10 = 42.6 (not a whole number)

Continuing this process with each integer all the way up to 426, we will find a variety of divisors. For this example, from our calculations, we found the following divisors so far: 1, 2, 3, and 6.

Continuing with integers beyond 10, we would find additional divisors, but for brevity’s sake, we’ll list out the complete set at the end.

After performing all the calculations, the entire list of divisors for 426 is as follows:

1, 2, 3, 6, 71, 142, 213, and 426.

These numbers can divide 426 without leaving a remainder, making them the divisors of 426. Understanding divisors helps in many areas of math, including simplifying fractions and solving equations.