# Factors of 242

Factors of 242 are 1, 2, 11, 22, 121, and 242

#### How to find factors of a number

 1.   Find factors of 242 using Division Method 2.   Find factors of 242 using Prime Factorization 3.   Find factors of 242 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 242

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

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

#### 2. Steps to find factors of 242 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 242 using the division method, follow these steps:

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

So, the prime factorization of 242 is, 242 = 2 x 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 242 as shown below:

So, the prime factorization of 242 is, 242 = 2 x 11 x 11.

#### 3. Find factors of 242 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 242 would be the two numbers which, when multiplied, give 242 as the result.

The following table represents the calculation of factors of 242 in pairs:

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

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 242. They are called negative pair factors.

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

#### 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. 242 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, 11, 22, 121, 242 are exact divisors of 242.
• 1 is a factor of every number. Eg. 1 is a factor of 242.
• Every number is a factor of zero (0), since 242 x 0 = 0.

• What is prime factorization of 242?

Prime factorization of 242 is 2 x 11 x 11.

• How do you find factors of a negative number? ( eg. -242 )?

Factors of -242 are -1, -2, -11, -22, -121, -242.

• What are the prime factors of 242?

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

• What are pair factors of 242?

The pair factors of 242 are (1,242), (2,121), (11,22).

• What is the greatest prime factors of 242?

The greatest prime factor of 242 is 11.

• What are six multiples of 242?

First five multiples of 242 are 484, 726, 968, 1210, 1452, 1694.

• What are factors of 242?

Factors of 242 are 1, 2, 11, 22, 121, 242.

• Which is the smallest prime factor of 242?

Smallest prime factor of 242 is 2.

• Is 242 a whole number?

Yes 242 is a whole number.

#### Examples of Factors

Kevin has been asked to write 5 factor(s) of 242. Can you predict the answer?

5 factor(s) of 242 are 1, 2, 11, 22, 121.

Sammy is puzzled while calculating the prime factors of 242. Can you help him find them?

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

What is prime factorization of 242?

Prime factorization of 242 is 2 x 11 x 11 = 2 x 112.

Ariel has been assigned the task to find the product of all the prime factors of 242. Can you help her?

Prime factors of 242 are 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 242?

Factors of 242 are 1, 2, 11, 22, 121, 242.
Even factors of 242 are 2, 22, 242.
Hence, product of even factors of 242 is; 2 x 22 x 242 = 10648.

Joy wants to calculate mean of all the factors of 242. Help him in finding the mean of 242.

Factors of 242 are 1, 2, 11, 22, 121, 242.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 242 is 1 + 2 + 11 + 22 + 121 + 242 = 399.
Hence, the mean of factors of 242 is 399 ÷ 6 = 66.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 242? Help her in writing all the factors.

Positive factors are 1, 2, 11, 22, 121, 242.
Negative factors are -1, -2, -11, -22, -121, -242.