Divisors of 961

Divisors of a number are the integers that can divide that number without leaving any remainder. Understanding divisors is important in mathematics as it helps us explore factors, simplify fractions, and solve various mathematical problems. In this article, we will discuss the concept of divisors in simple terms, using the number 961 as our main example.

To understand divisors better, we first need to talk about division. In division, we have three important terms:

• Dividend: This is the number we want to divide. For example, in the case of our number 961, this is the dividend.
• Divisor: This is the number by which we are dividing.
• Quotient: This is the result we get after dividing the dividend by the divisor.

Let’s write out an example using our number 961. If we want to divide 961 by 1, we can show this as:
961 / 1 = 961

In this case, 961 is the dividend, 1 is the divisor, and 961 is the quotient.

Now let’s look at how to find the divisors of 961. We’ll do this by dividing 961 by every integer from 1 up to 961. If the result (quotient) is a whole number, then that integer is a divisor of 961.

Step-by-Step Guide to Calculate the Divisors of 961

1. Start with 1 and divide 961 by it.
2. Move to the next integer (2) and repeat the process.
3. Continue this way until you reach 961, checking each time if the quotient is a whole number.

Now let’s perform these calculations:

1. 961 / 1 = 961 (whole number)
2. 961 / 2 = 480.5 (not a whole number)
3. 961 / 3 = 320.3333… (not a whole number)
4. 961 / 4 = 240.25 (not a whole number)
5. 961 / 5 = 192.2 (not a whole number)
6. 961 / 6 = 160.1666… (not a whole number)
7. 961 / 7 = 137.2857… (not a whole number)
8. 961 / 8 = 120.125 (not a whole number)
9. 961 / 9 = 106.7777… (not a whole number)
10. 961 / 31 = 31 (whole number)

Continuing this process for integers up to 961 allows us to find all the divisors. Here are some of the working results, showing only those integers that give a whole number as a quotient:

• 961 / 1 = 961 (divisor)
• 961 / 31 = 31 (divisor)
• 961 / 961 = 1 (divisor)

Conclusion

The complete list of divisors for 961, based on our calculations, is:

• 1
• 31
• 961

Thus, the divisors of 961 are 1, 31, and 961. Understanding how to calculate and identify divisors helps in many areas of mathematics.