# Factors of 434

Factors of 434 are 1, 2, 7, 14, 31, 62, 217, and 434

#### How to find factors of a number

 1.   Find factors of 434 using Division Method 2.   Find factors of 434 using Prime Factorization 3.   Find factors of 434 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 434

• Divide 434 by 1: 434 ÷ 1 : Remainder = 0
• Divide 434 by 2: 434 ÷ 2 : Remainder = 0
• Divide 434 by 7: 434 ÷ 7 : Remainder = 0
• Divide 434 by 14: 434 ÷ 14 : Remainder = 0
• Divide 434 by 31: 434 ÷ 31 : Remainder = 0
• Divide 434 by 62: 434 ÷ 62 : Remainder = 0
• Divide 434 by 217: 434 ÷ 217 : Remainder = 0
• Divide 434 by 434: 434 ÷ 434 : Remainder = 0

Hence, Factors of 434 are 1, 2, 7, 14, 31, 62, 217, and 434

#### 2. Steps to find factors of 434 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 434 using the division method, follow these steps:

• Step 1. Start dividing 434 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 434, which is 2. Divide 434 by 2 to obtain the quotient (217).
434 ÷ 2 = 217
• Step 3. Repeat step 1 with the obtained quotient (217).
217 ÷ 7 = 31
31 ÷ 31 = 1

So, the prime factorization of 434 is, 434 = 2 x 7 x 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 434 as shown below:

So, the prime factorization of 434 is, 434 = 2 x 7 x 31.

#### 3. Find factors of 434 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 434 would be the two numbers which, when multiplied, give 434 as the result.

The following table represents the calculation of factors of 434 in pairs:

Factor Pair Pair Factorization
1 and 434 1 x 434 = 434
2 and 217 2 x 217 = 434
7 and 62 7 x 62 = 434
14 and 31 14 x 31 = 434

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 434. They are called negative pair factors.

Hence, the negative pairs of 434 would be ( -1 , -434 ) , ( -2 , -217 ) , ( -7 , -62 ) and ( -14 , -31 ) .

#### 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

• Each number is a factor of itself. Eg. 434 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 7, 14, 31, 62, 217, 434 are exact divisors of 434.
• 1 is a factor of every number. Eg. 1 is a factor of 434.
• Every number is a factor of zero (0), since 434 x 0 = 0.

• What two numbers make 434?

Two numbers that make 434 are 2 and 217.

• What is prime factorization of 434?

Prime factorization of 434 is 2 x 7 x 31.

• Write some multiples of 434?

First five multiples of 434 are 868, 1302, 1736, 2170.

• Which is the smallest prime factor of 434?

The smallest prime factor of 434 is 2.

• Is 434 a perfect square?

No 434 is not a perfect square.

• What is the sum of all factors of 434?

The sum of all factors of 434 is 768.

• What are factors of 434?

Factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434.

• How do you find factors of a negative number? ( eg. -434 )?

Factors of -434 are -1, -2, -7, -14, -31, -62, -217, -434.

• Is 434 a whole number?

Yes 434 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 434. Help him in finding the mean of 434.

Factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 434 is 1 + 2 + 7 + 14 + 31 + 62 + 217 + 434 = 768.
Hence, the mean of factors of 434 is 768 ÷ 8 = 96.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 434? Help her in writing all the factors.

Positive factors are 1, 2, 7, 14, 31, 62, 217, 434.
Negative factors are -1, -2, -7, -14, -31, -62, -217, -434.

Joey wants to write all the prime factors of 434 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 434 are 2, 7, 31.
So in exponential form it can be written as 2 x 7 x 31.

Kevin has been asked to write 7 factor(s) of 434. Can you predict the answer?

7 factor(s) of 434 are 1, 2, 7, 14, 31, 62, 217.

Sammy is puzzled while calculating the prime factors of 434. Can you help him find them?

Factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434.
Prime factors of 434 are 2, 7, 31

What is prime factorization of 434?

Prime factorization of 434 is 2 x 7 x 31 = 2 x 7 x 31.

Can you help Rubel to find out the product of the even factors of 434?

Factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434.
Even factors of 434 are 2, 14, 62, 434.
Hence, product of even factors of 434 is; 2 x 14 x 62 x 434 = 753424.