# Factors of 429

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

#### How to find factors of a number

 1.   Find factors of 429 using Division Method 2.   Find factors of 429 using Prime Factorization 3.   Find factors of 429 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 429

• Divide 429 by 1: 429 ÷ 1 : Remainder = 0
• Divide 429 by 3: 429 ÷ 3 : Remainder = 0
• Divide 429 by 11: 429 ÷ 11 : Remainder = 0
• Divide 429 by 13: 429 ÷ 13 : Remainder = 0
• Divide 429 by 33: 429 ÷ 33 : Remainder = 0
• Divide 429 by 39: 429 ÷ 39 : Remainder = 0
• Divide 429 by 143: 429 ÷ 143 : Remainder = 0
• Divide 429 by 429: 429 ÷ 429 : Remainder = 0

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

#### 2. Steps to find factors of 429 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 429 using the division method, follow these steps:

• Step 1. Start dividing 429 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 429, which is 3. Divide 429 by 3 to obtain the quotient (143).
429 ÷ 3 = 143
• Step 3. Repeat step 1 with the obtained quotient (143).
143 ÷ 11 = 13
13 ÷ 13 = 1

So, the prime factorization of 429 is, 429 = 3 x 11 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 429 as shown below:

So, the prime factorization of 429 is, 429 = 3 x 11 x 13.

#### 3. Find factors of 429 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 429 would be the two numbers which, when multiplied, give 429 as the result.

The following table represents the calculation of factors of 429 in pairs:

Factor Pair Pair Factorization
1 and 429 1 x 429 = 429
3 and 143 3 x 143 = 429
11 and 39 11 x 39 = 429
13 and 33 13 x 33 = 429

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 429. They are called negative pair factors.

Hence, the negative pairs of 429 would be ( -1 , -429 ) , ( -3 , -143 ) , ( -11 , -39 ) and ( -13 , -33 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 11, 13, 33, 39, 143, 429 are exact divisors of 429.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 429 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 429.

• How do you find factors of a negative number? ( eg. -429 )?

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

• What is the sum of all factors of 429?

The sum of all factors of 429 is 672.

• What is prime factorization of 429?

Prime factorization of 429 is 3 x 11 x 13.

• What are the pair factors of 429?

Pair factors of 429 are (1,429), (3,143), (11,39), (13,33).

• What are six multiples of 429?

First five multiples of 429 are 858, 1287, 1716, 2145, 2574, 3003.

• Is 429 a whole number?

Yes 429 is a whole number.

• Which is the smallest prime factor of 429?

Smallest prime factor of 429 is 3.

• What are five multiples of 429?

First five multiples of 429 are 858, 1287, 1716, 2145, 2574.

• Write all factors of 429?

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

#### Examples of Factors

Joey wants to write all the prime factors of 429 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 429 are 3, 11, 13.
So in exponential form it can be written as 3 x 11 x 13.

How many factors are there for 429?

Factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 429. Can you predict the answer?

7 factor(s) of 429 are 1, 3, 11, 13, 33, 39, 143.

Sammy is puzzled while calculating the prime factors of 429. Can you help him find them?

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

What is prime factorization of 429?

Prime factorization of 429 is 3 x 11 x 13 = 3 x 11 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 429. Can you help her?

Prime factors of 429 are 3, 11, 13.
Hence, the product of prime factors of 429.

Can you help Rubel to find out the product of the even factors of 429?

Factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429.
Even factors of 429 are 0.
Hence, product of even factors of 429 is; 0 = 0.