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Factors of 714: Prime Factorization, Methods, and Examples

Factors are a list of numbers that divide the given number leaving zero as the remainder. 714 is an even and composite number. It has 16 factors in total. 

The factors will be both positive and negative if the given number is achieved by multiplying two-factor integers.

Factors of 714

Here are the factors of number 714.

Factors of 714: 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714

Negative Factors of 714

The negative factors of 714 are similar to their positive aspects, just with a negative sign.

Negative Factors of 714: -1, -2, -3, -6, -7, -14, -17, -21, -34, -42, -51, -102, -119, -238, -357, and -714

Prime Factorization of 714

The prime factorization of 714 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 7 x 17

In this article, we will learn about the factors of 714 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 714?

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, and 714. These numbers are the factors as they do not leave any remainder when divided by 714.

The factors of 714 are classified as prime numbers and composite numbers. The prime factors of the number 714 can be determined using the prime factorization technique.

How To Find the Factors of 714?

You can find the factors of 714 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 714, create a list containing the numbers that are exactly divisible by 714 with zero remainders. One important thing to note is that 1 and 714 are the 714’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 714 are determined as follows:

\[\dfrac{714}{1} = 714\]

\[\dfrac{714}{2} = 357\]

\[\dfrac{714}{3} = 238\]

\[\dfrac{714}{6} = 119\]

\[\dfrac{714}{7} = 102\]

\[\dfrac{714}{14} = 51\]

\[\dfrac{714}{17} = 42\]

\[\dfrac{714}{21} = 34\]

\[\dfrac{714}{714} = 1\]

Therefore, 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, and 714 are the factors of 714.

Total Number of Factors of 714

For 714, there are 16 positive factors and 16 negative ones. So in total, there are 32 factors of 714. 

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 714 is given as:

Factorization of 714 is 1 x 2 x 3 x 7 x 17.

The exponent of 1, 2, 3, 7, and 17 is 1.

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

Therefore, the total number of factors of 714 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 714 by Prime Factorization

The number 714 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 714 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 714, 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 714 can be expressed as:

714 = 2 x 3 x 7 x 17

Factors of 714 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 714, the factor pairs can be found as:

1 x 714 = 714

2 x 357= 714

3 x 238 = 714

6 x 119 = 714

7 x 102 = 714

14 x 51 = 714

17 x 42 = 714

21 x 34 = 714

The possible factor pairs of 714 are given as (1, 714), (2, 357), (3, 238), (6, 119), (7, 102), (14, 51), (17, 42), and (21, 34).

All these numbers in pairs, when multiplied, give 714 as the product.

The negative factor pairs of 714 are given as:

-1 x -714 = 714

-2 x -357= 714

-3 x -238 = 714

-6 x -119 = 714

-7 x -102 = 714

-14 x -51 = 714

-17 x -42 = 714

-21 x -34 = 714

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, -7, -14, -17, -21, -34, -42, -51, -102, -119, -238, -357, and -714 are called negative factors of 714.

The list of all the factors of 714, including positive as well as negative numbers, is given below.

Factor list of 714: 1, -1, 2, -2, 3, -3, 6, -6, 7, -7, 14, -14, 17, -17, 21, -21, 34, -34, 42, -42, 51, -51, 102, -102, 119, -119, 238, -238, 357, -357, 714, and -714

Factors of 714 Solved Examples

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

Example 1

How many factors of 714 are there?

Solution

The total number of Factors of 714 is 32.

Factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, and 714.

Example 2

Find the factors of 714 using prime factorization.

Solution

The prime factorization of 714 is given as:

714 $\div$ 2 = 357

357 $\div$ 3 = 119 

119 $\div$ 7 = 17  

17 $\div$ 17 = 1 

So the prime factorization of 714 can be written as:

2 x 3 x 7 x 17 = 714

Factors of 713|Factors List| Factors of 715

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