# Factors of 484

Factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, and 484

#### How to find factors of a number

 1.   Find factors of 484 using Division Method 2.   Find factors of 484 using Prime Factorization 3.   Find factors of 484 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 484

• Divide 484 by 1: 484 ÷ 1 : Remainder = 0
• Divide 484 by 2: 484 ÷ 2 : Remainder = 0
• Divide 484 by 4: 484 ÷ 4 : Remainder = 0
• Divide 484 by 11: 484 ÷ 11 : Remainder = 0
• Divide 484 by 22: 484 ÷ 22 : Remainder = 0
• Divide 484 by 44: 484 ÷ 44 : Remainder = 0
• Divide 484 by 121: 484 ÷ 121 : Remainder = 0
• Divide 484 by 242: 484 ÷ 242 : Remainder = 0
• Divide 484 by 484: 484 ÷ 484 : Remainder = 0

Hence, Factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, and 484

#### 2. Steps to find factors of 484 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 484 using the division method, follow these steps:

• Step 1. Start dividing 484 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 484, which is 2. Divide 484 by 2 to obtain the quotient (242).
484 ÷ 2 = 242
• Step 3. Repeat step 1 with the obtained quotient (242).
242 ÷ 2 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1

So, the prime factorization of 484 is, 484 = 2 x 2 x 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 484 as shown below:

So, the prime factorization of 484 is, 484 = 2 x 2 x 11 x 11.

#### 3. Find factors of 484 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 484 would be the two numbers which, when multiplied, give 484 as the result.

The following table represents the calculation of factors of 484 in pairs:

Factor Pair Pair Factorization
1 and 484 1 x 484 = 484
2 and 242 2 x 242 = 484
4 and 121 4 x 121 = 484
11 and 44 11 x 44 = 484
22 and 22 22 x 22 = 484

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 484. They are called negative pair factors.

Hence, the negative pairs of 484 would be ( -1 , -484 ) , ( -2 , -242 ) , ( -4 , -121 ) , ( -11 , -44 ) and ( -22 , -22 ) .

#### 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. 484 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 484.
• Every number is a factor of zero (0), since 484 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, 11, 22, 44, 121, 242, 484 are exact divisors of 484.
• Factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484. Each factor divides 484 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 11, 22, 44, 121, 242, 484 are all less than or equal to 484.

• Which is the smallest prime factor of 484?

The smallest prime factor of 484 is 2.

• Is 484 a whole number?

Yes 484 is a whole number.

• What are the prime factors of 484?

The factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484.
Prime factors of 484 are 2, 2, 11, 11.

• What two numbers make 484?

Two numbers that make 484 are 2 and 242.

• What are multiples of 484?

First five multiples of 484 are 968, 1452, 1936, 2420.

• What is the sum of all factors of 484?

The sum of all factors of 484 is 931.

• What are five multiples of 484?

First five multiples of 484 are 968, 1452, 1936, 2420, 2904.

• Is 484 a perfect square?

Yes 484 is a perfect square.

• What is the greatest prime factors of 484?

The greatest prime factor of 484 is 11.

#### Examples of Factors

How many factors are there for 484?

Factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484.
So there are in total 9 factors.

Kevin has been asked to write 8 factor(s) of 484. Can you predict the answer?

8 factor(s) of 484 are 1, 2, 4, 11, 22, 44, 121, 242.

Sammy is puzzled while calculating the prime factors of 484. Can you help him find them?

Factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484.
Prime factors of 484 are 2, 2, 11, 11

What is prime factorization of 484?

Prime factorization of 484 is 2 x 2 x 11 x 11 = 22 x 112.

Ariel has been assigned the task to find the product of all the prime factors of 484. Can you help her?

Prime factors of 484 are 2, 2, 11, 11.
Hence, the product of prime factors of 22.

Can you help Rubel to find out the product of the even factors of 484?

Factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484.
Even factors of 484 are 2, 4, 22, 44, 242, 484.
Hence, product of even factors of 484 is; 2 x 4 x 22 x 44 x 242 x 484 = 907039232.

Joy wants to calculate mean of all the factors of 484. Help him in finding the mean of 484.

Factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 484 is 1 + 2 + 4 + 11 + 22 + 44 + 121 + 242 + 484 = 931.
Hence, the mean of factors of 484 is 931 ÷ 9 = 103.44.