# Factors of 522

Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, and 522

#### How to find factors of a number

 1.   Find factors of 522 using Division Method 2.   Find factors of 522 using Prime Factorization 3.   Find factors of 522 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 522

• Divide 522 by 1: 522 ÷ 1 : Remainder = 0
• Divide 522 by 2: 522 ÷ 2 : Remainder = 0
• Divide 522 by 3: 522 ÷ 3 : Remainder = 0
• Divide 522 by 6: 522 ÷ 6 : Remainder = 0
• Divide 522 by 9: 522 ÷ 9 : Remainder = 0
• Divide 522 by 18: 522 ÷ 18 : Remainder = 0
• Divide 522 by 29: 522 ÷ 29 : Remainder = 0
• Divide 522 by 58: 522 ÷ 58 : Remainder = 0
• Divide 522 by 87: 522 ÷ 87 : Remainder = 0
• Divide 522 by 174: 522 ÷ 174 : Remainder = 0
• Divide 522 by 261: 522 ÷ 261 : Remainder = 0
• Divide 522 by 522: 522 ÷ 522 : Remainder = 0

Hence, Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, and 522

#### 2. Steps to find factors of 522 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 522 using the division method, follow these steps:

• Step 1. Start dividing 522 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 522, which is 2. Divide 522 by 2 to obtain the quotient (261).
522 ÷ 2 = 261
• Step 3. Repeat step 1 with the obtained quotient (261).
261 ÷ 3 = 87
87 ÷ 3 = 29
29 ÷ 29 = 1

So, the prime factorization of 522 is, 522 = 2 x 3 x 3 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 522 as shown below:

So, the prime factorization of 522 is, 522 = 2 x 3 x 3 x 29.

#### 3. Find factors of 522 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 522 would be the two numbers which, when multiplied, give 522 as the result.

The following table represents the calculation of factors of 522 in pairs:

Factor Pair Pair Factorization
1 and 522 1 x 522 = 522
2 and 261 2 x 261 = 522
3 and 174 3 x 174 = 522
6 and 87 6 x 87 = 522
9 and 58 9 x 58 = 522
18 and 29 18 x 29 = 522

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 522. They are called negative pair factors.

Hence, the negative pairs of 522 would be ( -1 , -522 ) , ( -2 , -261 ) , ( -3 , -174 ) , ( -6 , -87 ) , ( -9 , -58 ) and ( -18 , -29 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 522 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, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522 are exact divisors of 522.
• 1 is a factor of every number. Eg. 1 is a factor of 522.
• Every number is a factor of zero (0), since 522 x 0 = 0.

• Which is the smallest prime factor of 522?

Smallest prime factor of 522 is 2.

• Is 522 a perfect square?

No 522 is not a perfect square.

• What are five multiples of 522?

First five multiples of 522 are 1044, 1566, 2088, 2610, 3132.

• What is prime factorization of 522?

Prime factorization of 522 is 2 x 3 x 3 x 29.

• What are factors of 522?

Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.

• How do you find factors of a negative number? ( eg. -522 )?

Factors of -522 are -1, -2, -3, -6, -9, -18, -29, -58, -87, -174, -261, -522.

• Is 522 a whole number?

Yes 522 is a whole number.

• Which is greatest factor of 522?

The greatest factor of 522 is 261.

• What are the prime factors of 522?

The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.
Prime factors of 522 are 2, 3, 3, 29.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 522. Can you help her?

Prime factors of 522 are 2, 3, 3, 29.
Hence, the product of prime factors of 174.

Can you help Rubel to find out the product of the even factors of 522?

Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.
Even factors of 522 are 2, 6, 18, 58, 174, 522.
Hence, product of even factors of 522 is; 2 x 6 x 18 x 58 x 174 x 522 = 1137893184.

Joy wants to calculate mean of all the factors of 522. Help him in finding the mean of 522.

Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 522 is 1 + 2 + 3 + 6 + 9 + 18 + 29 + 58 + 87 + 174 + 261 + 522 = 1170.
Hence, the mean of factors of 522 is 1170 ÷ 12 = 97.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 522? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.
Negative factors are -1, -2, -3, -6, -9, -18, -29, -58, -87, -174, -261, -522.

How many factors are there for 522?

Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.
So there are in total 12 factors.

Joey wants to write all the prime factors of 522 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 522 are 2, 3, 3, 29.
So in exponential form it can be written as 2 x 32 x 29.

Kevin has been asked to write 11 factor(s) of 522. Can you predict the answer?

11 factor(s) of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261.