Divisors of 429

Divisors of a Number

When we talk about the divisors of a number, we are referring to the numbers that can be multiplied together to produce the original number. In simpler terms, if you can divide a number by another whole number and get a whole number as a result, then that other number is a divisor. This article will help you understand what divisors are, how to find them, and give you specific examples using the number 429.

To understand divisors better, we need to know a little bit about division. When you divide a number, you are splitting it into equal parts. In division, we have three main terms:

• Dividend: This is the number you are dividing.
• Divisor: This is the number you are dividing by.
• Quotient: This is the result you get after dividing.

Let’s take the number 429 as our example. If we have the equation 429 / 3 = 143, here:

• 429 is the dividend,
• 3 is the divisor,
• 143 is the quotient.

Now, let’s find all the divisors of 429. We will do this by checking every whole number from 1 up to 429 to see if it divides 429 evenly, meaning the quotient is a whole number.

Step-by-Step Guide to Calculate the Divisors of 429:

1. Start with 1, and divide 429 by 1.
2. Check the next whole number, 2, and divide 429 by 2.
3. Continue this process for each whole number up to 429.

Here is a detailed list of division calculations to see which numbers divide 429 evenly:

1. 429 / 1 = 429 (whole number)
2. 429 / 2 = 214.5 (not a whole number)
3. 429 / 3 = 143 (whole number)
4. 429 / 4 = 107.25 (not a whole number)
5. 429 / 5 = 85.8 (not a whole number)
6. 429 / 6 = 71.5 (not a whole number)
7. 429 / 7 = 61.2857 (not a whole number)
8. 429 / 8 = 53.625 (not a whole number)
9. 429 / 9 = 47.6667 (not a whole number)
10. 429 / 10 = 42.9 (not a whole number)

We found that the numbers 1 and 3 give us a whole number as a quotient. We can keep going, but for brevity, we’ll just mention that there are more divisors.

Continuing this process, we would find:

• 429 / 11 = 39 (whole number)
• 429 / 13 = 33 (whole number)
• 429 / 19 = 22.5789 (not a whole number)
• … and so on, until we reach 429.

Ultimately, the complete list of divisors of 429 is:

1, 3, 11, 13, 33, 39, 143, 429

To conclude, the divisors of 429 are:

• 1
• 3
• 11
• 13
• 33
• 39
• 143
• 429

These numbers can be multiplied in different combinations to recreate the number 429. Understanding divisors is helpful in many areas of math, including fractions, prime factorization, and even problem-solving strategies!