Maths

Divisors of 117

by Staff Writer
3 min read

Divisors of a number are the integers that can be divided evenly into that number, meaning the result of the division is a whole number without any leftovers. Understanding divisors helps in various areas of math, including simplifying fractions, finding greatest common factors, and working with multiples. In this article, we will focus on the divisors of the number 117.

To start, let’s talk about division so we can understand how divisors work. Division is the process of splitting a number into equal parts. In the division equation, there are three key terms:

  • Dividend: This is the number we want to divide. For example, in dividing 117 by 3, 117 is the dividend.
  • Divisor: This is the number we are dividing by. In the same example, 3 is the divisor.
  • Quotient: This is the result of the division. Using the previous example, 117 divided by 3 gives us 39 as the quotient.

So, we can write the equation like this:
117 / 3 = 39

Now, let’s find out the divisors of 117 by dividing it by every integer from 1 up to 117. We will check which of these divisions result in a whole number.

Here’s how to calculate the divisors step by step:

  1. Start with 1 and go up to 117.
  2. Divide 117 by each integer.
  3. Check if the result (the quotient) is a whole number.

Now, let’s perform the division calculations:

  1. 117 / 1 = 117 (Whole number)
  2. 117 / 2 = 58.5 (Not a whole number)
  3. 117 / 3 = 39 (Whole number)
  4. 117 / 4 = 29.25 (Not a whole number)
  5. 117 / 5 = 23.4 (Not a whole number)
  6. 117 / 6 = 19.5 (Not a whole number)
  7. 117 / 7 = 16.7142857 (Not a whole number)
  8. 117 / 8 = 14.625 (Not a whole number)
  9. 117 / 9 = 13 (Whole number)
  10. 117 / 10 = 11.7 (Not a whole number)
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Continuing this process would eventually yield additional whole number quotients such as:

  1. 117 / 13 = 9 (Whole number)
  2. 117 / 39 = 3 (Whole number)
  3. 117 / 117 = 1 (Whole number)

Now, we have found the divisors that produce whole number quotients.

Divisors of 117:

  • 1
  • 3
  • 9
  • 13
  • 39
  • 117

In conclusion, the entire list of divisors of 117 is:
1, 3, 9, 13, 39, 117

Understanding divisors is essential in mathematics as it helps in various calculations and problem-solving techniques. We hope this simple guide has made it easier for you to understand the concept of divisors!

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