# Factors of 868

Factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, and 868

#### How to find factors of a number

 1.   Find factors of 868 using Division Method 2.   Find factors of 868 using Prime Factorization 3.   Find factors of 868 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 868

• Divide 868 by 1: 868 ÷ 1 : Remainder = 0
• Divide 868 by 2: 868 ÷ 2 : Remainder = 0
• Divide 868 by 4: 868 ÷ 4 : Remainder = 0
• Divide 868 by 7: 868 ÷ 7 : Remainder = 0
• Divide 868 by 14: 868 ÷ 14 : Remainder = 0
• Divide 868 by 28: 868 ÷ 28 : Remainder = 0
• Divide 868 by 31: 868 ÷ 31 : Remainder = 0
• Divide 868 by 62: 868 ÷ 62 : Remainder = 0
• Divide 868 by 124: 868 ÷ 124 : Remainder = 0
• Divide 868 by 217: 868 ÷ 217 : Remainder = 0
• Divide 868 by 434: 868 ÷ 434 : Remainder = 0
• Divide 868 by 868: 868 ÷ 868 : Remainder = 0

Hence, Factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, and 868

#### 2. Steps to find factors of 868 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 868 using the division method, follow these steps:

• Step 1. Start dividing 868 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 868, which is 2. Divide 868 by 2 to obtain the quotient (434).
868 ÷ 2 = 434
• Step 3. Repeat step 1 with the obtained quotient (434).
434 ÷ 2 = 217
217 ÷ 7 = 31
31 ÷ 31 = 1

So, the prime factorization of 868 is, 868 = 2 x 2 x 7 x 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 868 as shown below:

So, the prime factorization of 868 is, 868 = 2 x 2 x 7 x 31.

#### 3. Find factors of 868 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 868 would be the two numbers which, when multiplied, give 868 as the result.

The following table represents the calculation of factors of 868 in pairs:

Factor Pair Pair Factorization
1 and 868 1 x 868 = 868
2 and 434 2 x 434 = 868
4 and 217 4 x 217 = 868
7 and 124 7 x 124 = 868
14 and 62 14 x 62 = 868
28 and 31 28 x 31 = 868

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 868. They are called negative pair factors.

Hence, the negative pairs of 868 would be ( -1 , -868 ) , ( -2 , -434 ) , ( -4 , -217 ) , ( -7 , -124 ) , ( -14 , -62 ) and ( -28 , -31 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 868 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 868.
• Every number is a factor of zero (0), since 868 x 0 = 0.
• 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, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868 are exact divisors of 868.
• Factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868. Each factor divides 868 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868 are all less than or equal to 868.

• Is 868 a perfect square?

No 868 is not a perfect square.

• What are factors of 868?

Factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.

• Which is greatest factor of 868?

The greatest factor of 868 is 434.

• What is the sum of all factors of 868?

The sum of all factors of 868 is 1792.

• What are multiples of 868?

First five multiples of 868 are 1736, 2604, 3472, 4340.

• What is the greatest prime factors of 868?

The greatest prime factor of 868 is 31.

• What are six multiples of 868?

First five multiples of 868 are 1736, 2604, 3472, 4340, 5208, 6076.

• What is prime factorization of 868?

Prime factorization of 868 is 2 x 2 x 7 x 31.

• Is 868 a whole number?

Yes 868 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 868? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.
Negative factors are -1, -2, -4, -7, -14, -28, -31, -62, -124, -217, -434, -868.

Can you help Sammy find out the product of the odd factors of 868?

Factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.
Odd factors of 868 are 1, 7, 31, 217.
Hence product of odd factors of 868 is; 1 x 7 x 31 x 217 = 47089.

Joey wants to write all the prime factors of 868 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 868 are 2, 2, 7, 31.
So in exponential form it can be written as 22 x 7 x 31.

How many factors are there for 868?

Factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 868. Can you predict the answer?

11 factor(s) of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434.

Sammy is puzzled while calculating the prime factors of 868. Can you help him find them?

Factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.
Prime factors of 868 are 2, 2, 7, 31

What is prime factorization of 868?

Prime factorization of 868 is 2 x 2 x 7 x 31 = 22 x 7 x 31.