# Factors of 870

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

#### How to find factors of a number

 1.   Find factors of 870 using Division Method 2.   Find factors of 870 using Prime Factorization 3.   Find factors of 870 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 870

• Divide 870 by 1: 870 ÷ 1 : Remainder = 0
• Divide 870 by 2: 870 ÷ 2 : Remainder = 0
• Divide 870 by 3: 870 ÷ 3 : Remainder = 0
• Divide 870 by 5: 870 ÷ 5 : Remainder = 0
• Divide 870 by 6: 870 ÷ 6 : Remainder = 0
• Divide 870 by 10: 870 ÷ 10 : Remainder = 0
• Divide 870 by 15: 870 ÷ 15 : Remainder = 0
• Divide 870 by 29: 870 ÷ 29 : Remainder = 0
• Divide 870 by 30: 870 ÷ 30 : Remainder = 0
• Divide 870 by 58: 870 ÷ 58 : Remainder = 0
• Divide 870 by 87: 870 ÷ 87 : Remainder = 0
• Divide 870 by 145: 870 ÷ 145 : Remainder = 0
• Divide 870 by 174: 870 ÷ 174 : Remainder = 0
• Divide 870 by 290: 870 ÷ 290 : Remainder = 0
• Divide 870 by 435: 870 ÷ 435 : Remainder = 0
• Divide 870 by 870: 870 ÷ 870 : Remainder = 0

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

#### 2. Steps to find factors of 870 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 870 using the division method, follow these steps:

• Step 1. Start dividing 870 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 870, which is 2. Divide 870 by 2 to obtain the quotient (435).
870 ÷ 2 = 435
• Step 3. Repeat step 1 with the obtained quotient (435).
435 ÷ 3 = 145
145 ÷ 5 = 29
29 ÷ 29 = 1

So, the prime factorization of 870 is, 870 = 2 x 3 x 5 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 870 as shown below:

So, the prime factorization of 870 is, 870 = 2 x 3 x 5 x 29.

#### 3. Find factors of 870 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 870 would be the two numbers which, when multiplied, give 870 as the result.

The following table represents the calculation of factors of 870 in pairs:

Factor Pair Pair Factorization
1 and 870 1 x 870 = 870
2 and 435 2 x 435 = 870
3 and 290 3 x 290 = 870
5 and 174 5 x 174 = 870
6 and 145 6 x 145 = 870
10 and 87 10 x 87 = 870
15 and 58 15 x 58 = 870
29 and 30 29 x 30 = 870

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 870. They are called negative pair factors.

Hence, the negative pairs of 870 would be ( -1 , -870 ) , ( -2 , -435 ) , ( -3 , -290 ) , ( -5 , -174 ) , ( -6 , -145 ) , ( -10 , -87 ) , ( -15 , -58 ) and ( -29 , -30 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 870 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870 are exact divisors of 870.
• 1 is a factor of every number. Eg. 1 is a factor of 870.
• Every number is a factor of zero (0), since 870 x 0 = 0.

• How do you find factors of a negative number? ( eg. -870 )?

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

• What is the sum of all factors of 870?

The sum of all factors of 870 is 2160.

• What is prime factorization of 870?

Prime factorization of 870 is 2 x 3 x 5 x 29.

• What are the pair factors of 870?

Pair factors of 870 are (1,870), (2,435), (3,290), (5,174), (6,145), (10,87), (15,58), (29,30).

• What are six multiples of 870?

First five multiples of 870 are 1740, 2610, 3480, 4350, 5220, 6090.

• Is 870 a whole number?

Yes 870 is a whole number.

• Which is the smallest prime factor of 870?

Smallest prime factor of 870 is 2.

• What are five multiples of 870?

First five multiples of 870 are 1740, 2610, 3480, 4350, 5220.

• Write all factors of 870?

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

#### Examples of Factors

Joey wants to write all the prime factors of 870 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 870 are 2, 3, 5, 29.
So in exponential form it can be written as 2 x 3 x 5 x 29.

How many factors are there for 870?

Factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 870. Can you predict the answer?

15 factor(s) of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435.

Sammy is puzzled while calculating the prime factors of 870. Can you help him find them?

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

What is prime factorization of 870?

Prime factorization of 870 is 2 x 3 x 5 x 29 = 2 x 3 x 5 x 29.

Ariel has been assigned the task to find the product of all the prime factors of 870. Can you help her?

Prime factors of 870 are 2, 3, 5, 29.
Hence, the product of prime factors of 870.

Can you help Rubel to find out the product of the even factors of 870?

Factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870.
Even factors of 870 are 2, 6, 10, 30, 58, 174, 290, 870.
Hence, product of even factors of 870 is; 2 x 6 x 10 x 30 x 58 x 174 x 290 x 870 = 9166361760000.