Divisors of 1260

When we talk about divisors of a number, we are referring to the numbers that can divide that number evenly, without leaving a remainder. For example, if we say that 3 is a divisor of 12, it means that when we divide 12 by 3, we get a whole number (which is 4). In this article, we will explore what divisors are, how to find them, and specifically look at the divisors of the number 1260.

To understand divisors better, let’s look at the concept of division. In a division statement, there are three important terms: the "dividend," the "divisor," and the "quotient."

• The dividend is the number you want to divide.
• The divisor is the number you are dividing by.
• The quotient is the result of the division.

For example, if we want to divide 1260 by 1, we can express this as:

1260 / 1 = 1260

In this case:

• The dividend is 1260,
• The divisor is 1, and
• The quotient is 1260.

Now, let’s figure out how to calculate the divisors of 1260. To find the divisors, we will divide 1260 by every integer from 1 up to 1260. We are looking for those integers (divisors) that give us whole number results when we divide.

Here is a step-by-step guide to calculating the divisors of 1260:

1. Start with 1 and divide 1260 by that number. If you get a whole number, then that number is a divisor.
2. Move to the next integer (2) and repeat the process.
3. Keep going until you reach 1260.

Let’s calculate some divisors of 1260 by performing these divisions:

1. 1260 / 1 = 1260 (whole number)
2. 1260 / 2 = 630 (whole number)
3. 1260 / 3 = 420 (whole number)
4. 1260 / 4 = 315 (whole number)
5. 1260 / 5 = 252 (whole number)
6. 1260 / 6 = 210 (whole number)
7. 1260 / 7 = 180 (whole number)
8. 1260 / 8 = 157.5 (not a whole number)
9. 1260 / 9 = 140 (whole number)
10. 1260 / 10 = 126 (whole number)

Keep going like this, and soon you’ll find more divisors. The process continues, but for now, we will stop here.

Now let’s list the results we found, specifying which divisions produce whole numbers:

1. 1260 / 1 = 1260 (divisor)
2. 1260 / 2 = 630 (divisor)
3. 1260 / 3 = 420 (divisor)
4. 1260 / 4 = 315 (divisor)
5. 1260 / 5 = 252 (divisor)
6. 1260 / 6 = 210 (divisor)
7. 1260 / 7 = 180 (divisor)
8. 1260 / 8 = 157.5 (not a divisor)
9. 1260 / 9 = 140 (divisor)
10. 1260 / 10 = 126 (divisor)

Continuing this method, we would determine all the divisors of 1260.

In conclusion, the full list of divisors for the number 1260 is:

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 36, 42, 60, 63, 70, 84, 90, 105, 126, 140, 180, 252, 315, 420, 630, and 1260.

These numbers are all the integers that can divide 1260 evenly, showcasing the complete set of its divisors. This understanding helps us appreciate the relationships between numbers.