# Factors of 121—with division and prime factorization

## Factors of 121

The factors of 121 are the real numbers that divide the original number completely.

If we divide 121 by any one of its factors, then the remainder will be zero and the quotient will be a whole number. As an example, 3 is the factor of 9 as when we divide 9 by 3, we get;

9 divided by 3 ⇒ 9 ÷ 3 = 3

Hence, the quotient after division is a whole number.

It is also possible to state that if two numbers are multiplied together, they constitute 121. As 121 is a product of prime factors, it is also known as the original number.

## What are Factors of -121?

When we multiply two numbers, and we get -121 as a product, that numbers are the factors of -121.

Here is the explanation:

-1 × 121 = -121

1 × -121 = -121

-11 × 11 = -121

11 × -11 = -121

We can get -121 by having (-1, 121), and(-11, 11) as a pair of factors. Similarly, we can also get -121 by having (1, -121), and(11, -11) as a pair of factors.

## How to Find Factors of 121?

There are factors of 121 that divide an original number without leaving a remainder. In this case, we will divide 121 by the smallest natural number. We know that 121 is an odd number, so we cannot divide it by an even number.

121 ÷ 1 = 121

121 ÷ 11 = 11

121 ÷ 121 = 1

The quotient of 121 divided by any other number will be a fraction and not a whole number.

For example, 121 divided by 10 is 12.1.

Therefore, only 1, 11, and 121 are factors of 121.

## Pair Factors of 121

If we want to find the pair factors of 121, we must find the product of the two numbers.

1 × 121 = 121

11 × 11 = 121

Thus, the pair factors are (1, 121) and (11, 11). As we can see, the pair factors are both positive.

Similarly, the multiplication of two negative factors of 121 will also result in a positive value if we consider negative pair factors of 121.

-1 × -121 = 121

-11 × -11 = 121

Thus, the negative pair factors are (-1, -121) and (-11, -11).

## Prime Factorization of 121

We need to divide 121 starting with the smallest prime number until the remainder is 1, in order to find the prime factors. Due to the fact that 121 is divisible by 11 and no other primes are smaller than 11;

Step 1: Taking 121 and dividing it by the smallest prime factor, 11, we get;

121/11 = 11

Step 2: Divide 11 by the smallest prime factor, again 11, to get;

11/11 = 1

Step 3: It is now impossible to divide 1 further. Hence,

## Solved Examples

Q.1: If there are 121 oranges to be distributed among 11 children. How many pens does each student get?

Solution:

Given,

Number of oranges = 121

Number of children = 11

Each of the children will get = 121/11 = 11 oranges.

Q.2: How much is the sum of all the factors of 121?

Solution: There are three factors to 121: 1, 11 and 121.

Sum = 1+11+121 = 133

Hence, 133 is the required sum.

Q.3: Calculate the common factors of 101 and 121?

Solution: To find the common factors of 101 and 121, we must first determine the factors of each of the numbers.

The prime number 101 has only two factors, because it is a prime number.

101 → 1, 101

However, 121 is a composite number, therefore factors of:

121 → 1, 11 and 121

Therefore, we can see, the common factor is only 1.

## FAQ`s

### 1. How many factors of 121 are there?

There are three factors in 121. These are 1, 11 and 121.

### 2. Are the multiples and factors of 121 the same?

No. There are different factors and multiples for all natural numbers. There are only three factors of 121, but there are indefinitely many multiples.

### 3. What are the multiples of 121?

First 10 multiples of 121 = 1121, 242, 363, 484, 605, 726, 847, 968, 1089 and 1210.

### 4. What are the prime factors of 121?

Prime factorization of 121 = 11 × 11 = 112. Hence, 11 is the prime factor of 121.

### 5. What is the average value of factors of one hundred and twenty-one?

The average value is equal to the sum of all the values divided by the total number of values

Average (factors of 121) = (1+11+121)/3 = 133/3