# Factors of 702: Prime Factorization, Methods, and Examples

702 is an even number that is divisible by 2 completely as well as it is composite means it has more than two factors.

When multiply factor pair of 702 gives 702 in return.

### Factors of 702

Here are the factors of number 702.

Factors of 702:

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, and 702

### Negative Factors of 702

The negative factors of 702 are similar to its positive aspects, just with a negative sign.

Negative Factors of 702:

-1, -2,-3, -6, -9, -13, -18, -26, -27, -39, -54, -78,- 117, -234, -351, and -702

### Prime Factorization of 702

The prime factorization of 702 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 3 x 3 x 13

In this article, we will learn about the factors of 702 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 702?

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, and 702. These numbers are the factors as they do not leave any remainder when divided by 702.

The factors of 702 are classified as prime numbers and composite numbers. The prime factors of the number 702 can be determined using the prime factorization technique.

## How To Find the Factors of 702?

You can find the factors of 702 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 702, create a list containing the numbers that are exactly divisible by 702 with zero remainders. One important thing to note is that 1 and 702 are the 702’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 702 are determined as follows:

$\dfrac{702}{1} = 702$

$\dfrac{702}{2} = 351$

$\dfrac{702}{3} = 234$

$\dfrac{702}{6} = 117$

$\dfrac{702}{9} = 78$

$\dfrac{702}{13} = 54$

$\dfrac{702}{18} = 39$

$\dfrac{702}{26} = 27$

$\dfrac{702}{27} = 26$

$\dfrac{702}{702} = 1$

Therefore, 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, and 702 are the factors of 702.

### Total Number of Factors of 702

For 702, there are 16 positive factors and 16 negative ones. So in total, there are 32 factors of 702.

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 702 is given as:

Factorization of 702 is 2 x 3 x 3 x 3 x 13.

The exponent of 2, 3, and 13 is 1,3,1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 702 is 32 whereas16 are 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 702 by Prime Factorization

The number 702 is a composite. 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 702 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 702, 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 702 can be expressed as:

702 = 2 x 3 x 3 x 3 x 13

## Factors of 702 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 702, the factor pairs can be found as:

1 x 702 = 702

2 x 351 = 702

3 x 234 = 702

6 x 117 = 702

9 x 78 = 702

13 x 54 = 702

18 x 39 = 702

26 x 27 = 702

The possible factor pairs of 702 are given as (1, 702), (2, 351), (3, 234), (6, 117), (9, 78), (13, 54), (18, 39) and (26, 27).

All these numbers in pairs, when multiplied, give 702 as the product.

The negative factor pairs of 702 are given as:

-1 x -702 = 702

-2 x -351 = 702

-3 x -234 = 702

-6 x -117 = 702

-9 x -78 = 702

-13 x -54 = 702

-18 x -39 = 702

-26 x -27 = 702

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,-3, -6, -9, -13, -18, -26, -27, -39, -54, -78,- 117, -234, -351, and -702 are called negative factors of 702.

The list of all the factors of 702, including positive as well as negative numbers, is given below.

Factor list of 702: 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 13, -13, 18, -18, 26, -26, 27, -27, 39, -39, 54, -54, 78, -78, 117, -117, 234, -234, 351, -351, 702 and -702 are the factors of 702

## Factors of 702 Solved Examples

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

### Example 1

How many factors of 702 are there?

### Solution

The total number of Factors of 702 is 16.

Factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, and 702.

### Example 2

Find the factors of 702 using prime factorization.

### Solution

The prime factorization of 702 is given as:

702 $\div$ 2 = 351

351 $\div$ 3 = 117

117 $\div$ 3 = 39

39 $\div$ 3 = 13

13 $\div$ 13 = 1

So the prime factorization of 702 can be written as:

2 x 3 x 3 x 3 x 13  = 702