 # Factors of 532: Prime Factorization, Methods, and Examples

The integers that divide 532 evenly and without leaving any remainder are known as factors of 532. Since 532 is an even number, it can be divided by 2 and has a 2 as its smallest prime factor. A total of 12 factors make up the number 532, with 532 being the largest.

### Factors of 532

Here are the factors of number 532.

Factors of 532 : 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266 and 532

### Negative Factors of 532

The negative factors of 532  are similar to their positive aspects, just with a negative sign.

Negative Factors of 532 : -1, -2,- 4, -7, -14, -19, -28, -38, -76, -133, -266 and -532

### Prime Factorization of 532

The prime factorization of 532  is the way of expressing its prime factors in the product form.

Prime Factorization: 22 x 71 x 191

In this article, we will learn about the factors of 532 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 532?

The factors of 532 are1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266 and 532. These numbers are the factors as they do not leave any remainder when divided by 532.

The factors of 532  are classified as prime numbers and composite numbers. The prime factors of the number 532 can be determined using the prime factorization technique.

## How To Find the Factors of 532?

You can find the factors of 532  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 532, create a list containing the numbers that are exactly divisible by 532  with zero remainders. One important thing to note is that 1 and 532 are the 532 ‘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 X are determined as follows:

$\dfrac{532 }{1} = 532$

$\dfrac{532 }{2} = 266$

$\dfrac{532 }{4} = 133$

$\dfrac{532 }{7 } = 76$

$\dfrac{532 }{14} =38$

$\dfrac{532 }{19} =28$

$\dfrac{532 }{28} = 19$

$\dfrac{532 }{38 } = 14$

$\dfrac{532 }{76} = 7$

$\dfrac{532 }{133} = 4$

$\dfrac{532 }{266} = 2$

$\dfrac{532 }{532 } = 1$

Therefore, 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266 and 532  are the factors of 532.

### Total Number of Factors of 532

For 532, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 532.

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 532 is given as:

Factorization of 532 is 22 x 71 x 191.

The exponent of 2 is 2, 7 is 1, and 19 is 1.

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

Therefore, the total number of factors of 532 is 24. 12 is positive, and 12 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 532 by Prime Factorization

The number 532   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 532 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 532, 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 532  can be expressed as:

532 = 22 x 71 x 191

## Factors of 532 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 532 , the factor pairs can be found as:

1 x 532 = 532

2 x 266 = 532

4 x 133 = 532

7 x 76 = 532

14 x 38 = 532

19 x 28 = 532

The possible factor pairs of 532 are given as (1, 532 ), (2, 266),(4, 133),(7, 76)(14, 38)and (19, 28).

All these numbers in pairs, when multiplied, give 532 as the product.

The negative factor pairs of 532 are given as:

-1 x -532 = 532

-2 x -266 = 532

-4 x -133 = 532

-7 x- 76 = 532

-14 x- 38 = 532

-19 x -28 = 532

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, -2,- 4, -7, -14, -19, -28, -38, -76, -133, -266 and -532 are called negative factors of 532.

The list of all the factors of 532, including positive as well as negative numbers, is given below.

Factor list of 532 :1.-1, 2,-2,4,-4, 7,-7, 14,-14, 19,-19,28, -28, 38,-38, -76, 133,-133, 266,-266, 532 , and -532

## Factors of 532 Solved Examples

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

### Example 1

How many factors of 532 are there?

### Solution

The total number of Factors of 532 is 24.

Factors of 532 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266 and 532.

### Example 2

Find the factors of 532 using prime factorization.

### Solution

The prime factorization of 532 is given as:

532 $\div$ a = v

v $\div$ v = 1

So the prime factorization of 532 can be written as:

22 x 71 x 191 = 532