Factors of 429: Prime Factorization, Methods, and Examples

The integers that leave zero as the remainder are the factors of 429. Any integer’s factors can be found in various ways, including the division method and the prime factorization method.Â

Both positive and negative elements may be present.

Factors of 429

Here are the factors of number 429.

Factors of 429: 1, 3, 11, 13, 33, 39, 143 and 429

Negative Factors of 429

The negative factors of 429 are similar to their positive aspects, just with a negative sign.

Negative Factors of 429: -1, -3, -11, -13, -33, -39, -143 and -429

Prime Factorization of 429

The prime factorization of 429Â is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 11 x 13Â

In this article, we will learn about the factors of 429 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 429?

The factors 429 are 1, 3, 11, 13, 33, 39, 143, and 429. These numbers are the factors as they do not leave any remainder when divided by 429.

The factors 429Â are classified as prime numbers and composite numbers. The prime factors of the number 429 can be determined using the prime factorization technique.

How To Find the Factors of 429?

You can find the factors of 429Â by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 429, create a list containing the numbers that are exactly divisible by 429 with zero remainders. One important thing to note is that 1 and 429 are the 429’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 429 are determined as follows:

$\dfrac{429}{1} = 429$

$\dfrac{429}{3} = 143$

$\dfrac{429}{11} = 39$

$\dfrac{429}{13} = 33$

$\dfrac{429}{33} = 13$

$\dfrac{429}{39} = 11$

$\dfrac{429}{143} = 3$

$\dfrac{429}{429} = 1$

Therefore, 1, 3, 11, 13, 33, 39, 143 and 429are the factors of 429.

Total Number of Factors of 429

For 429, there are 8Â positive factors and 8Â negative ones. So in total, there are 16 factors of 429.Â

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 429 is given as:

Factorization of 429 is 1, 3, 11, 13, 33, 39, 143 and 429.

The exponent of 1, 3, 11, 13, 33, 39, 143, and 429 is 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 429 is 16. 8 is positive, and 8 factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 429 by Prime Factorization

The number 429 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 429 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 429, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 429Â can be expressed as:

429 = 3 x 11 x 13Â

Factors of 429 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 429, the factor pairs can be found as:

1 x 429 = 429

3 x 143 = 429

11 x 39= 429

13 x 33 = 429

The possible factor pairs of 429 are given as (1, 429), (3, 143), (11, 39), and (13, 33).

All these numbers in pairs, when multiplied, give 429 as the product.

The negative factor pairs of 429 are given as:

-1 x -429 = 429

-3 x -143 = 429

-11 x -39= 429

-13 x -33 = 429

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -3, -11, -13, -33, -39, -143 and -429 are called negative factors of 429.

The list of all the factors of 429, including positive as well as negative numbers, is given below.

Factor list of 429: 1,-1, 3,-3, 11,-11, 13,-13, 33,-33, 39,-39, 143,-143 ,429 and -429

Factors of 429 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 429 are there?

Solution

The total number of Factors of 429 is 16.

Factors of 429 are 1, 3, 11, 13, 33, 39, 143 and 429.

Example 2

Find the factors of 429 using prime factorization.

Solution

The prime factorization of 429 is given as:

429 $\div$ 3 = 143

143 $\div$ 11 = 13

13$\div$ 13 = 1

So the prime factorization of 429 can be written as:

3 x 11 x 13Â = 429