Factors of 880: Prime Factorization, Methods, and Examples

The lists of numbers that leave no remainders when divided by 880 are known as the factors of 880. There are both positive and negative 880 factors. 

The number 880 is both a composite number and an even number.

Factors of 880

Here are the factors of number 880.

Factors of 880: 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440 and 880

Negative Factors of 880

The negative factors of 880 are similar to its positive aspects, just with a negative sign.

Negative Factors of 880: -1, -2, -4,-5, -8, -10, -11, -16, -20,-22, -40, -44, -55, -80, -88, -110, -176, -220, -440 and -880

Prime Factorization of 880

The prime factorization of 880 is the way of expressing its prime factors in the product form.

Prime Factorization: 2⁴ x 5¹ x 11¹

In this article, we will learn about the factors of 880 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 880?

The factors of 880 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440 and 880. These numbers are the factors as they do not leave any remainder when divided by 880.

The factors of 880 are classified as prime numbers and composite numbers. The prime factors of the number 880 can be determined using the prime factorization technique.

How To Find the Factors of 880?

You can find the factors of 880 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 880, create a list containing the numbers that are exactly divisible by 880 with zero remainders. One important thing to note is that 1 and 880 are the 880’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 880 are determined as follows:

\[\dfrac{880}{1} = 880\]

\[\dfrac{880}{2} = 440\]

\[\dfrac{880}{4} = 220\]

\[\dfrac{880}{5} = 176\]

\[\dfrac{880}{8} = 110\]

\[\dfrac{880}{10} = 88\]

\[\dfrac{880}{11} = 80\]

\[\dfrac{880}{16} = 50\]

\[\dfrac{880}{20} = 44\]

\[\dfrac{880}{22} = 40\]

\[\dfrac{880}{40} = 22\]

\[\dfrac{880}{44} = 20\]

\[\dfrac{880}{50} = 16\]

\[\dfrac{880}{80} = 11\]

\[\dfrac{880}{88} = 10\]

\[\dfrac{880}{110} = 8\]

\[\dfrac{880}{176} = 5\]

\[\dfrac{880}{220} = 4\]

\[\dfrac{880}{440} = 2\]

\[\dfrac{880}{880} = 1\]

Therefore, 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440 and 880 are the factors of 880.

Total Number of Factors of 880

For 880, there are 20 positive factors and 20 negative ones. So in total, there are 40 factors out of 880. 

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 880 is given as:

Factorization of 880 is 2⁴ x 5¹ x 11¹.

The exponent of 2 is 4, 5 is 1, and 11 is 1.

Adding 1 to each and multiplying them together results in 40.

Therefore, the total number of factors of 880 is 40. 20 are positive, and 20 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 880 by Prime Factorization

The number 880 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 880 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 880, 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 880 can be expressed as:

880 = 2⁴ x 5¹ x 11¹

Factors of 880 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 880, the factor pairs can be found as:

1 x 880 = 880

2 x 440 = 880

4 x 220 = 880

5 x 176 = 880

8 x 110 = 880

10 x 88 = 880

11 x 80 = 880

16 x 55 = 880

20 x 44 = 880

22 x 40 = 880

The possible factor pairs of 880 are given as (1, 880),(2, 440),(4, 220),(5, 176),(8, 110),(10, 88),(11, 80),(16, 55),(20, 44) and (22, 40).

All these numbers in pairs, when multiplied, give 880 as the product.

The negative factor pairs of 880 are given as:

-1 x -880 = 880

-2 x -440 = 880

-4 x -220 = 880

-5 x -176 = 880

-8 x -110 = 880

-10 x -88 = 880

-11 x -80 = 880

-16 x -55 = 880

-20 x -44 = 880

-22 x -40 = 880

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, -11, -16, -20,-22, -40, -44, -55, -80, -88, -110, -176, -220, -440 and -880 are called negative factors of 880.

The list of all the factors of 880, including positive as well as negative numbers, is given below.

Factor list of 880: 1,-1, 2,-2, 4,-4,5,-5, 8,-8, 10,-10, 11,-11, 16,-16, 20,-20,22,-22, 40,-40, 44,-44, 55,-55, 80,-80, 88,-88, 110,-110, -176,176, 220,-220, 440,-440, 880, and -880

Factors of 880 Solved Examples

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

Example 1

How many factors of 880 are there?

Solution

The total number of Factors of 880 is 40.

Factors of 880 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440 and 880.

Example 2

Find the factors of 880 using prime factorization.

Solution

The prime factorization of 880 is given as:

880 $\div$ 2 = 440 

440 $\div$ 2 = 220 

220 $\div$ 2 = 110

110 $\div$ 2 = 55

55 $\div$ 5 = 11

11 $\div$ 11 = 1

So the prime factorization of 880 can be written as:

2⁴ x 5¹ x 11¹ = 880

Factors of 879|Factors List| Factors of 881