Factors of 524: Prime Factorization, Methods, and Examples

The numbers that, when 524  is used as the dividend, leave zero as the remainder are considered to be the factors of 524. 

Factors Of 524

As long as the supplied number is obtained by multiplying two-factor integers, the factors of the given number may be both positive and negative.

Factors of 524

Here are the factors of number 524.

Factors of 524:  1, 2, 4, 131, 262, 524

Negative Factors of524

The negative factors of 524 are similar to its positive aspects, just with a negative sign.

Negative Factors of 524:-1, -2, -4, -131, -262 and -524

Prime Factorization of 524

The prime factorization of 524 is the way of expressing its prime factors in the product form.

Prime Factorization: 22 x 1311

In this article, we will learn about the factors of 524 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 524?

The factors of 524 are  1, 2, 4, 131, 262, and 524. These numbers are the factors as they do not leave any remainder when divided by524.

The factors of524 are classified as prime numbers and composite numbers. The prime factors of the number 524 can be determined using the prime factorization technique.

How To Find the Factors of 524?

You can find the factors of524 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 524, create a list containing the numbers that are exactly divisible by 524 with zero remainders. One important thing to note is that 1 and 524 are the 524’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 of524 are determined as follows:

\[\dfrac{524}{1} = 524\]

\[\dfrac{524}{2} = 262\]

\[\dfrac{524}{4} = 131\]

\[\dfrac{524}{131} = 4\]

\[\dfrac{524}{262} = 2\]

\[\dfrac{524}{524} = 1\]

Therefore, 1, 2, 4, 131, 262, and 524 are the factors of 524.

Total Number of Factors of 524

For 524, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 524. 

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 524 is given as:

The factorization of 524 is 22 x 1311.

The exponent of 2 is 2, and 131 is 1.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 524 is 12. 6 is positive, and 6 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 524 by Prime Factorization

The number 524 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.prime factorization of 524

Before finding the factors of 524 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 524, 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 524 can be expressed as:

524 = 22 x 1311

Factors of 524 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.Factors of 524 in Pairs

For 524, the factor pairs can be found as:

1 x 524 = 524

2 x 262 = 524

4 x 131= 524

The possible factor pairs of 524 are given as (1, 524), (2, 262), and (4, 131).

All these numbers in pairs, when multiplied, give 524 as the product.

The negative factor pairs of 524 are given as:

-1 x -524 = 524

-2 x -262 = 524

-4 x -131= 524

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, -131, -262 and -524 are called negative factors of 524.

The list of all the factors of 524, including positive as well as negative numbers, is given below.

Factor list of 524:  1,-1, 2,-2, 4,-4, 131,-131, 262,-262, 524, and -524

Factors of 524 Solved Examples

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

Example 1

How many factors of 524 are there?


The total number of Factors of 524 is 12.

Factors of 524 are  1, 2, 4, 131, 262, 524.

Example 2

Find the factors of 524 using prime factorization.


The prime factorization of 524 is given as:

524 $\div$ 2 = 262

262 $\div$ 2 = 131

131 $\div$ 131 = 1

So the prime factorization of 524 can be written as:

22 x 1311= 524

Factors of 523|Factors List| Factors of 525