Maths

Divisors of 63

by Staff Writer
3 min read

Divisors are the numbers that can divide another number without leaving a remainder. In simpler terms, if you can split a number evenly, those numbers you used to split it are called its divisors. Understanding divisors is important in many areas of math, including fractions, ratios, and number theory. In this article, we will focus on finding the divisors of the number 63, and we will take you through each step clearly.

To understand what a divisor is, we first need to talk a bit about division. Division is like breaking something into equal parts. In a division problem, there are three key terms:

  1. Dividend: This is the number you want to divide. For example, in 63 divided by 7, 63 is the dividend.
  2. Divisor: This is the number you are dividing by. In our example, 7 is the divisor.
  3. Quotient: This is the result of the division. In our example, 63 divided by 7 equals 9, so 9 is the quotient.

So, the division can be written like this:
63 / 7 = 9

Now, let’s move on to calculating the divisors of 63 step by step. To find all divisors of 63, we will divide the number 63 by every integer starting from 1 up to 63. If the result is a whole number (without any decimals), that integer is a divisor of 63.

  1. Start with 1:

    • 63 / 1 = 63 (whole number, so 1 is a divisor)

  2. Next, try 2:

    • 63 / 2 = 31.5 (not a whole number, so 2 is not a divisor)

  3. Next, try 3:

    • 63 / 3 = 21 (whole number, so 3 is a divisor)

  4. Next, try 4:

    • 63 / 4 = 15.75 (not a whole number, so 4 is not a divisor)

  5. Next, try 5:

    • 63 / 5 = 12.6 (not a whole number, so 5 is not a divisor)

  6. Next, try 6:

    • 63 / 6 = 10.5 (not a whole number, so 6 is not a divisor)

  7. Next, try 7:

    • 63 / 7 = 9 (whole number, so 7 is a divisor)

  8. Next, try 8:

    • 63 / 8 = 7.875 (not a whole number, so 8 is not a divisor)

  9. Next, try 9:

    • 63 / 9 = 7 (whole number, so 9 is a divisor)
  10. Lastly, try 10:
    • 63 / 10 = 6.3 (not a whole number, so 10 is not a divisor)
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Continuing this process would result in more divisors. However, since there are many possible integers to try, we will stop here. The other potential numbers beyond 10 will produce either larger divisors or we might find the same divisors we’ve already listed.

Here is a summary of our findings where we only noted the divisors that produced whole numbers:

  • 1 (63 / 1 = 63)
  • 3 (63 / 3 = 21)
  • 7 (63 / 7 = 9)
  • 9 (63 / 9 = 7)
  • 21 (63 / 3 = 21)
  • 63 (63 / 1 = 63)

The divisors of 63, therefore, are:
1, 3, 7, 9, 21, 63

In conclusion, understanding divisors can help us see how numbers relate to each other. In this case, for the number 63, the complete list of divisors is:
1, 3, 7, 9, 21, 63.

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