 # Factors of 122

In Mathematics, factors of 122 are the numbers that divide the original number, evenly or uniformly. Alternatively, we can also say, if the product of two natural numbers is equal to 122, then they are the factors. Since 122 is a composite number, it has more than two factors. We can evaluate the factors by the simple division method. If the quotient obtained is a whole number and remainder is zero, then divisor is a factor.

Let us find the factors of 122 here in this article, along with pair factors and prime factors.

 Factors Pair Factors Prime Factors Form 1, 2, 61 and 122 (1, 122) and (2, 61) 122 = 2 x 61

## How to Find Factors of 122?

Factors of 122 are the real numbers that can divide 122, completely. By factorising means, breaking a number in the form of a product of two or more numbers. Thus, we have to divide 122 by its factors to check if it is divisible or not. Now, let us find the factors here.

122 ÷ 1 = 122

122 ÷ 2 = 61

122 ÷ 61 = 2

122 ÷ 122 = 1

In all the above four divisions we can see, the remainders are zero and quotients are the whole numbers. Thus, the factors of 122 are 1, 2, 61 and 122.

## Pair Factors of 122

When two numbers are multiplied and result in 122, then the two numbers are the factors of 122 in pairs.

1 × 122 = 122

2 × 61 = 122

Therefore, the pair factors are (1, 122) and (2, 61).

Now, if we consider the negative pair factors, then the multiplication of negative numbers will result in a positive number. Thus,

-1 × -122 = 122

-2 × -61 = 122

Therefore, the negative pair factors are (-1, -122) and (-2, -61).

## Prime Factorisation of 122

Prime factors of 122 are the primes that can divide the original number into an equal number of parts. The list of prime numbers from 1 to 122 is given below to figure out the prime factors.

List of prime numbers (Between 1 and 122) :

 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113

Step 1: 122 is the even number. Thus it is divisible by 2.

122/2 = 61

Step 2: Now from the list of prime numbers, we can see, 61 itself is a prime number, therefore,

61/61 = 1

We cannot divide further since the dividend is equal to 1 and it is divisible by 1 only.

Therefore, the prime factors are 2 and 61.

 Prime factorisation of 122 = 2 x 61

## Solved Examples

Q.1: Find the sum of all the factors of 122. Also, find the average.

Solution: The factors of 122 are 1, 2, 61 and 122 .

Sum = 1 + 2 + 61 + 122 = 186

Therefore, 186 is the required sum.

Average = Sum of all values ÷ Total number of values

Hence,

Average = 186 ÷ 4 = 46.5

Thus, 46.5 is the required average.

Q.2: What are the greatest common factors of 120 and 122?

Answer: Let us write first, the factors of both the numbers.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors of 122 are 1, 2, 61, 122

Then the greatest common factor is 2.

Q.3: What are the common factors of 100, 122, 140 and 142?

Answer: Listing the factors of all the given numbers.

The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100

The factors of 122 are 1, 2, 61, 122

The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

The factors of 142 are 1, 2, 71, 142

Therefore, Common factors are 1 and 2.

## Frequently Asked Questions on Factors of 122

### What are the factors of 122?

There are a total of four factors of 122. These factors are 1, 2, 61 and 122.

### What is 122 as a product of prime factors?

The prime factor form of 122 is: 2 x 61.

### What are the multiples of 122?

The first ten multiples of 122 are 122, 244, 366, 488, 610, 732, 854, 976, 1098 and 1220.

### Is 122 prime or composite?

122 is a composite number, since it has more than two factors.

### Is 4 a factor of 122?

4 is not a factor of 122. If we divide 122 by 4, then the result is a fraction.

122/4 = 30.5.

### Is 122 a perfect square?

No, 122 is not a perfect square because the root of 122 will not result in a whole number.

√122 = 11.045