# Factors of 121 in pair

Factors of 121 in pair are (1, 121) , (11, 11)

#### How to find factors of a number in pair

 1.   Steps to find factors of 121 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 121 in pair

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 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 121 are 1 , 11 , 121. So, factors of 121 in pair are (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.

#### Steps to find Factors of 121

• Step 1. Find all the numbers that would divide 121 without leaving any remainder. Starting with the number 1 upto 60 (half of 121). The number 1 and the number itself are always factors of the given number.
121 ÷ 1 : Remainder = 0
121 ÷ 11 : Remainder = 0
121 ÷ 121 : Remainder = 0

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

• Is there any even prime factor of 121?

No there is no even prime factor, i.e. 2, of 121.

• What is the mean of all prime factors of 121?

Factors of 121 are 1 , 11 , 121. Prime factors of 121 are 11 , 11. Therefore mean of prime factors of 121 is (11 + 11) / 2 = 11.00.

• What is the mean of factors of 121?

Factors of 121 are 1 , 11 , 121. therefore mean of factors of 121 is (1 + 11 + 121) / 3 = 44.33.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Can you help Rubel in arranging 121 blocks in order to form a rectangle in all possible ways? For arranging 121 blocks in order to form a rectangle in all possible ways we need to find factors of 121 in pair.

Factors of 121 are 1, 11, 121. So, factors of 121 in pair are (1,121), (11,11).

How many total number of factors of 121 in pair are possible?

Factors of 121 are 1, 11, 121. Hence, the factors of 121 in pair are (1,121), (11,11). Therefore, in total 2 pairs of factors are possible.

Sammy wants to write all the negative factors of 121 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 121 are -1, -11, -121. Hence, factors of 121 in pair are (-1,-121), (-11,-11).

Find the product of all prime factors of 121.

Factors of 121 are 1, 11, 121. Prime factors are 11, 11. So, the product of all prime factors of 121 would be 11 x 11 = 121.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 121.
- Writing all prime factors of 121.
- Writing all the possible factors of 121 in pair.
Help him in writing all these.

Positive factors of 121 are 1, 11, 121.
Prime factors of 121 are 11, 11.
Factors of 121 in pair are (1,121), (11,11).

Can you help Sammy list the factors of 121 and also find the factor pairs?

Factors of 121 are 1, 11, 121.
Factors of 121 in pair are (1,121), (11,11).

Help Diji in finding factors of 121 by Prime Factorization method and then sorting factors of 121 in pairs.

Prime factorization of 121 is 11 x 11. Factors of 121 in pair can be written as (1,121), (11,11).

Write the smallest prime factor of 121.

Smallest prime factor of 121 is 11.