Factors of 680: Prime Factorization, Methods, and Examples

The factors are those numbers that leave a zero remainder and a whole number quotient when divided by the given number. The factors of 680 are numbers that completely divide it without leaving any remainder. 

Its factors are both positive and negative.

Factors of 680

Here are the factors of number 680.

Factors of 680: 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

Negative Factors of 680

The negative factors of 680 are similar to its positive aspects, just with a negative sign.

Negative Factors of 680: -1, -2, -4, -5, -8, -10, -17, -20, -34, -40, -68, -85, -136, -170, -340, and -680

Prime Factorization of 680

The prime factorization of 680 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 5 x 17

In this article, we will learn about the factors of 680 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 680?

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, and 680. These numbers are the factors as they do not leave any remainder when divided by 680.

The factors of 680 are classified as prime numbers and composite numbers. The prime factors of the number 680 can be determined using the prime factorization technique.

How To Find the Factors of 680?

You can find the factors of 680 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 680, create a list containing the numbers that are exactly divisible by 680 with zero remainders. One important thing to note is that 1 and 680 are the 680’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 680 are determined as follows:

\[\dfrac{680}{1} = 680\]

\[\dfrac{680}{2} = 340\]

\[\dfrac{680}{4} = 170\]

\[\dfrac{680}{5} = 136\]

\[\dfrac{680}{8} = 85\]

\[\dfrac{680}{10} = 68\]

\[\dfrac{680}{17} = 40\]

\[\dfrac{680}{20} = 34\]

\[\dfrac{680}{680} = 1\]

Therefore, 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, and 680 are the factors of 680.

Total Number of Factors of 680

For 680, there are 16 positive factors and 16 negative ones. So in total, there are 32 factors of 680. 

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 680 is given as:

Factorization of 680 is 1 x 2 x 2 x 2 x 5 x 17.

The exponent of 1, 2, 5, and 17 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 680 is 32. 16 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 680 by Prime Factorization

The number 680 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 680 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 680, 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 680 can be expressed as:

680 = 2 x 2 x 2 x 5 x 17

Factors of 680 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 680, the factor pairs can be found as:

1 x 680 = 680

2 x 340 = 680

4 x 170 = 680

5 x 136  = 680

8 x 85 = 680

10 x 68 = 680

17 x 40 = 680

20 x 34 = 680

The possible factor pairs of 680 are given as (1, 680), (2, 340), (4, 170), (5, 136), (8, 85), (10, 68), (17, 40), and (20, 34).

All these numbers in pairs, when multiplied, give 680 as the product.

The negative factor pairs of 680 are given as:

-1 x -680 = 680

-2 x -340 = 680

-4 x -170 = 680

-5 x -136  = 680

-8 x -85 = 680

-10 x -68 = 680

-17 x -40 = 680

-20 x -34 = 680

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, -5, -8, -10, -17, -20, -34, -40, -68, -85, -136, -170, -340, and -680 are called negative factors of 680.

The list of all the factors of 680, including positive as well as negative numbers, is given below.

Factor list of 680: 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 17, -17, 20, -20, 34, -34, 40, -40, 68, -68, 85, -85, 136, -136, 170, -170, 340, -340, 680, and -680

Factors of 680 Solved Examples

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

Example 1

How many factors of 680 are there?

Solution

The total number of Factors of 680 is 32.

Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, and 680.

Example 2

Find the factors of 680 using prime factorization.

Solution

The prime factorization of 680 is given as:

680 $\div$ 2 = 340 

340 $\div$ 2 = 170 

170 $\div$ 2 = 85 

85 $\div$ 5 = 17 

17 $\div$ 17 = 1 

So the prime factorization of 680 can be written as:

2 x 2 x 2 x 5 x 17 = 680

Factors of 679|Factors List| Factors of 681