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Factors of 870: Prime Factorization, Methods, and Examples

There is a total of 16 numbers on the number line that are said to be the factors of 870. All these 17 numbers leave ne remainder when 870 is divided by them. 

The list includes prime and composite numbers listed below: 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870.

Factors of 870

Here are the factors of number 870.

Factors of 870: 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870

Negative Factors of 870

The negative factors of 870 are similar to its positive aspects, just with a negative sign.

Negative Factors of 870: -1, -2, -3, -5, -6, -10, -15, -29, -30, -58, -87, -145, -174, -290, -435, -870

Prime Factorization of 870

The prime factorization of 870 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 5 x 29

In this article, we will learn about the factors of 870 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 870?

The factors of 870 are  1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870 . These numbers are the factors as they do not leave any remainder when divided by 870.

The factors of 870 are classified as prime numbers and composite numbers. The prime factors of the number 870 can be determined using the prime factorization technique.

How To Find the Factors of 870?

You can find the factors of 870 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 870, create a list containing the numbers that are exactly divisible by 870 with zero remainders. One important thing to note is that 1 and 870 are the 870’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 870 are determined as follows:

\[\dfrac{870}{1} = 870\]

\[\dfrac{870}{2} = 435\]

\[\dfrac{870}{3} = 290\]

\[\dfrac{870}{5} = 174\]

\[\dfrac{870}{6} = 145\]

\[\dfrac{870}{10} = 87\]

\[\dfrac{870}{15} = 58\]

\[\dfrac{870}{29} = 30\]

\[\dfrac{870}{30} = 29\]

\[\dfrac{870}{58} = 15\]

\[\dfrac{870}{87} = 10\]

\[\dfrac{870}{145} = 6\]

\[\dfrac{870}{174} = 5\]

\[\dfrac{870}{290} = 3\]

\[\dfrac{870}{435} = 2\]

\[\dfrac{870}{870} = 1\]

Therefore, 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870 are the factors of 870.

Total Number of Factors of 870

For 870, there are 16 positive factors and 16 negative ones. So in total, there are 32 factors of 870. 

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 870 is given as:

Factorization of 870 is 1 x 2 x 3 x 5 x 29.

The exponent of 1, 2, 3, 5, and 29 is 1.

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

Therefore, the total number of factors of 870 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 870 by Prime Factorization

The number 870 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 870 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 870, 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 870 can be expressed as:

870 = 2 x 3 x 5 x 29

Factors of 870 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 870, the factor pairs can be found as:

1 x 870 = 870

2 x 435 = 870

3 x 290 = 870

5 x 174 = 870

6 x 145 = 870

10 x 87 = 870

15 x 58 = 870

29 x 30 = 870

The possible factor pairs of 870 are given as (1, 870), (2, 435), (3, 290), (5, 174), (6, 145), (10, 87), (15, 58), and (29, 30).

All these numbers in pairs, when multiplied, give 870 as the product.

The negative factor pairs of 870 are given as:

-1 x -870 = 870

-2 x- 435 = 870

-3 x -290 = 870

-5 x -174 = 870

-6 x -145 = 870

-10 x -87 = 870

-15 x -58 = 870

-29 x -30 = 870

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, -5, -6, -10, -15, -29, -30, -58, -87, -145, -174, -290, -435, and -870 are called negative factors of 870.

The list of all the factors of 870, including positive as well as negative numbers, is given below.

Factor list of 870:  1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 29, -29, 30, -30, 58, -58, 87, -87, 145, -145, 174, -174, 290, -290, 435, -435, 870, and -870

Factors of 870 Solved Examples

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

Example 1

How many factors of 870 are there?

Solution

The total number of Factors of 870 is 16.

Factors of 870 are  1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870.

Example 2

Find the factors of 870 using prime factorization.

Solution

The prime factorization of 870 is given as:

870 $\div$ 2 = 435 

435 $\div$ 3 = 145

145 $\div$ 5 = 29

29 $\div$ 29 = 1 

So the prime factorization of 870 can be written as:

2 x 3 x 5 x 7 = 870

Factors of 869|Factors List| Factors of 871

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