 # Factors of 616: Prime Factorization, Methods, and Examples

The factors of 616 are numbers that, when divided by 616, produce zero as the remainder. Such numbers divide 616 evenly. 616 is an even composite number having 16 positives and 16 negative factors. More details about the factorization method are provided in the article.

### Factors of 616

Here are the factors of number 616.

Factors of 616: 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616

### Negative Factors of 616

The negative factors of 616 are similar to its positive aspects, just with a negative sign.

Negative Factors of 616: -1, -2, -4, -7, -8, -11, -14, -22, -28, -44, -56, -77, -88, -154, -308, and -616

### Prime Factorization of 616

The prime factorization of 616 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 7 x 11

In this article, we will learn about the factors of 616 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 616?

The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, and 616. These numbers are the factors as they do not leave any remainder when divided by 616.

The factors of 616 are classified as prime numbers and composite numbers. The prime factors of the number 616 can be determined using the prime factorization technique.

## How To Find the Factors of 616?

You can find the factors of 616 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 616, create a list containing the numbers that are exactly divisible by 616 with zero remainders. One important thing to note is that 1 and 616 are the 616’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 616 are determined as follows:

$\dfrac{616}{1} = 616$

$\dfrac{616}{2} = 308$

$\dfrac{616}{4} = 154$

$\dfrac{616}{7} = 88$

$\dfrac{616}{8} = 77$

$\dfrac{616}{11} = 56$

$\dfrac{616}{14} = 44$

$\dfrac{616}{22} = 28$

$\dfrac{616}{28} = 22$

$\dfrac{616}{44} = 14$

$\dfrac{616}{56} = 11$

$\dfrac{616}{77} = 8$

$\dfrac{616}{88} = 7$

$\dfrac{616}{154} = 4$

$\dfrac{616}{108} = 2$

$\dfrac{616}{616} = 1$

Therefore, 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, and 616 are the factors of 616.

### Total Number of Factors of 616

For 616, there are 16 positive factors and 16 negative ones. So in total, there are 32 factors of 616.

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 616 is given as:

Factorization of 616 is 1 x 2 x 2 x 2 x 7 x 11.

The exponent of 1, 2, 7, and 11 is 1, 3, 1, and 1 respectively.

Adding 1 to each and multiplying them together results in 32.

Therefore, the total number of factors of 616 is 32. 16 is positive, and 16 factors are negative.

### Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

## Factors of 616 by Prime Factorization

The number 616 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors. Before finding the factors of 616 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 616, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 616 can be expressed as:

616 = 2 x 2 x 2 x 7 x 11

## Factors of 616 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given. For 616, the factor pairs can be found as:

1 x 616 = 616

2 x 308 = 616

4 x 154 = 616

7 x 88 = 616

8 x 77 = 616

11 x 56 = 616

14 x 44 = 616

22 x 28 = 616

The possible factor pairs of 616 are given as (1, 616), (2, 308), (4, 154), (7, 88), (8, 77), (11, 56), (14, 44), and (22, 28).

All these numbers in pairs, when multiplied, give 616 as the product.

The negative factor pairs of 616 are given as:

-1 x -616 = 616

-2 x -308 = 616

-4 x -154 = 616

-7 x -88 = 616

-8 x -77 = 616

-11 x -56 = 616

-14 x -44 = 616

-22 x -28 = 616

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -4, -7, -8, -11, -14, -22, -28, -44, -56, -77, -88, -154, -308, and -616 are called negative factors of 616.

The list of all the factors of 616, including positive as well as negative numbers, is given below.

Factor list of 616: 1, -1, 2, -2, 4, -4, 7, -7, 8, -8, 11, -11, 14, -14, 22, -22, 28, -28, 44, -44, 56, -56, 77, -77, 88, -88, 154, -154, 308, -308, 616, and -616

## Factors of 616 Solved Examples

To better understand the concept of factors, let’s solve some examples.

### Example 1

How many factors of 616 are there?

### Solution

The total number of Factors of 616 is 32.

Factors of 32 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, and 616.

### Example 2

Find the factors of 616 using prime factorization.

### Solution

The prime factorization of 616 is given as:

616 $\div$ 2 = 308

308 $\div$ 2 = 154

154 $\div$ 2 = 77

77 $\div$ 7 = 11

11 $\div$ 11 = 1

So the prime factorization of 616 can be written as:

2 x 2 x 2 x 7 x 11 = 615