# Factors of 121

Factors of 121 are 1, 11, and 121

#### How to find factors of a number

 1.   Find factors of 121 using Division Method 2.   Find factors of 121 using Prime Factorization 3.   Find factors of 121 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 121

• Divide 121 by 1: 121 ÷ 1 : Remainder = 0
• Divide 121 by 11: 121 ÷ 11 : Remainder = 0
• Divide 121 by 121: 121 ÷ 121 : Remainder = 0

Hence, Factors of 121 are 1, 11, and 121

#### 2. Steps to find factors of 121 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 121 using the division method, follow these steps:

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

So, the prime factorization of 121 is, 121 = 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 121 as shown below:

So, the prime factorization of 121 is, 121 = 11 x 11.

#### 3. Find factors of 121 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 121 would be the two numbers which, when multiplied, give 121 as the result.

The following table represents the calculation of factors of 121 in pairs:

Factor Pair Pair Factorization
1 and 121 1 x 121 = 121
11 and 11 11 x 11 = 121

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 121. They are called negative pair factors.

Hence, the negative pairs of 121 would be ( -1 , -121 ) , ( -11 , -11 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 11, 121 are exact divisors of 121.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 121 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 121.

• Is 121 a perfect square?

Yes 121 is a perfect square.

• What are factors of 121?

Factors of 121 are 1, 11, 121.

• Which is greatest factor of 121?

The greatest factor of 121 is 11.

• What is the sum of all factors of 121?

The sum of all factors of 121 is 133.

• What are multiples of 121?

First five multiples of 121 are 242, 363, 484, 605.

• What is the greatest prime factors of 121?

The greatest prime factor of 121 is 11.

• What are six multiples of 121?

First five multiples of 121 are 242, 363, 484, 605, 726, 847.

• What is prime factorization of 121?

Prime factorization of 121 is 11 x 11.

• Is 121 a whole number?

Yes 121 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 121? Help her in writing all the factors.

Positive factors are 1, 11, 121.
Negative factors are -1, -11, -121.

Can you help Sammy find out the product of the odd factors of 121?

Factors of 121 are 1, 11, 121.
Odd factors of 121 are 1, 11, 121.
Hence product of odd factors of 121 is; 1 x 11 x 121 = 1331.

Joey wants to write all the prime factors of 121 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 121 are 11, 11.
So in exponential form it can be written as 112.

How many factors are there for 121?

Factors of 121 are 1, 11, 121.
So there are in total 3 factors.

Kevin has been asked to write 2 factor(s) of 121. Can you predict the answer?

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

Sammy is puzzled while calculating the prime factors of 121. Can you help him find them?

Factors of 121 are 1, 11, 121.
Prime factors of 121 are 11, 11

What is prime factorization of 121?

Prime factorization of 121 is 11 x 11 = 112.