# Factors of 524

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

#### How to find factors of a number

 1.   Find factors of 524 using Division Method 2.   Find factors of 524 using Prime Factorization 3.   Find factors of 524 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 524

• Divide 524 by 1: 524 ÷ 1 : Remainder = 0
• Divide 524 by 2: 524 ÷ 2 : Remainder = 0
• Divide 524 by 4: 524 ÷ 4 : Remainder = 0
• Divide 524 by 131: 524 ÷ 131 : Remainder = 0
• Divide 524 by 262: 524 ÷ 262 : Remainder = 0
• Divide 524 by 524: 524 ÷ 524 : Remainder = 0

Hence, Factors of 524 are 1, 2, 4, 131, 262, and 524

#### 2. Steps to find factors of 524 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 524 using the division method, follow these steps:

• Step 1. Start dividing 524 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 524, which is 2. Divide 524 by 2 to obtain the quotient (262).
524 ÷ 2 = 262
• Step 3. Repeat step 1 with the obtained quotient (262).
262 ÷ 2 = 131
131 ÷ 131 = 1

So, the prime factorization of 524 is, 524 = 2 x 2 x 131.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 524 as shown below:

So, the prime factorization of 524 is, 524 = 2 x 2 x 131.

#### 3. Find factors of 524 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 524 would be the two numbers which, when multiplied, give 524 as the result.

The following table represents the calculation of factors of 524 in pairs:

Factor Pair Pair Factorization
1 and 524 1 x 524 = 524
2 and 262 2 x 262 = 524
4 and 131 4 x 131 = 524

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 524. They are called negative pair factors.

Hence, the negative pairs of 524 would be ( -1 , -524 ) , ( -2 , -262 ) and ( -4 , -131 ) .

#### 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. 524 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 524.
• Every number is a factor of zero (0), since 524 x 0 = 0.
• 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, 4, 131, 262, 524 are exact divisors of 524.
• Factors of 524 are 1, 2, 4, 131, 262, 524. Each factor divides 524 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 131, 262, 524 are all less than or equal to 524.

• What two numbers make 524?

Two numbers that make 524 are 2 and 262.

• What is prime factorization of 524?

Prime factorization of 524 is 2 x 2 x 131.

• Write some multiples of 524?

First five multiples of 524 are 1048, 1572, 2096, 2620.

• Which is the smallest prime factor of 524?

The smallest prime factor of 524 is 2.

• Is 524 a perfect square?

No 524 is not a perfect square.

• What is the sum of all factors of 524?

The sum of all factors of 524 is 924.

• What are factors of 524?

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

• How do you find factors of a negative number? ( eg. -524 )?

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

• Is 524 a whole number?

Yes 524 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 524. Help him in finding the mean of 524.

Factors of 524 are 1, 2, 4, 131, 262, 524.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 524 is 1 + 2 + 4 + 131 + 262 + 524 = 924.
Hence, the mean of factors of 524 is 924 ÷ 6 = 154.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 524? Help her in writing all the factors.

Positive factors are 1, 2, 4, 131, 262, 524.
Negative factors are -1, -2, -4, -131, -262, -524.

Joey wants to write all the prime factors of 524 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 524 are 2, 2, 131.
So in exponential form it can be written as 22 x 131.

Kevin has been asked to write 5 factor(s) of 524. Can you predict the answer?

5 factor(s) of 524 are 1, 2, 4, 131, 262.

Sammy is puzzled while calculating the prime factors of 524. Can you help him find them?

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

What is prime factorization of 524?

Prime factorization of 524 is 2 x 2 x 131 = 22 x 131.

Can you help Rubel to find out the product of the even factors of 524?

Factors of 524 are 1, 2, 4, 131, 262, 524.
Even factors of 524 are 2, 4, 262, 524.
Hence, product of even factors of 524 is; 2 x 4 x 262 x 524 = 1098304.