# Factors of 814

Factors of 814 are 1, 2, 11, 22, 37, 74, 407, and 814

#### How to find factors of a number

 1.   Find factors of 814 using Division Method 2.   Find factors of 814 using Prime Factorization 3.   Find factors of 814 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 814

• Divide 814 by 1: 814 ÷ 1 : Remainder = 0
• Divide 814 by 2: 814 ÷ 2 : Remainder = 0
• Divide 814 by 11: 814 ÷ 11 : Remainder = 0
• Divide 814 by 22: 814 ÷ 22 : Remainder = 0
• Divide 814 by 37: 814 ÷ 37 : Remainder = 0
• Divide 814 by 74: 814 ÷ 74 : Remainder = 0
• Divide 814 by 407: 814 ÷ 407 : Remainder = 0
• Divide 814 by 814: 814 ÷ 814 : Remainder = 0

Hence, Factors of 814 are 1, 2, 11, 22, 37, 74, 407, and 814

#### 2. Steps to find factors of 814 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 814 using the division method, follow these steps:

• Step 1. Start dividing 814 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 814, which is 2. Divide 814 by 2 to obtain the quotient (407).
814 ÷ 2 = 407
• Step 3. Repeat step 1 with the obtained quotient (407).
407 ÷ 11 = 37
37 ÷ 37 = 1

So, the prime factorization of 814 is, 814 = 2 x 11 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 814 as shown below:

So, the prime factorization of 814 is, 814 = 2 x 11 x 37.

#### 3. Find factors of 814 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 814 would be the two numbers which, when multiplied, give 814 as the result.

The following table represents the calculation of factors of 814 in pairs:

Factor Pair Pair Factorization
1 and 814 1 x 814 = 814
2 and 407 2 x 407 = 814
11 and 74 11 x 74 = 814
22 and 37 22 x 37 = 814

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 814. They are called negative pair factors.

Hence, the negative pairs of 814 would be ( -1 , -814 ) , ( -2 , -407 ) , ( -11 , -74 ) and ( -22 , -37 ) .

#### How can we define factors?

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

#### Properties of factors

• Each number is a factor of itself. Eg. 814 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, 11, 22, 37, 74, 407, 814 are exact divisors of 814.
• 1 is a factor of every number. Eg. 1 is a factor of 814.
• Every number is a factor of zero (0), since 814 x 0 = 0.

• Is 814 a perfect square?

No 814 is not a perfect square.

• What are factors of 814?

Factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814.

• Which is greatest factor of 814?

The greatest factor of 814 is 407.

• What is the sum of all factors of 814?

The sum of all factors of 814 is 1368.

• What are multiples of 814?

First five multiples of 814 are 1628, 2442, 3256, 4070.

• What is the greatest prime factors of 814?

The greatest prime factor of 814 is 37.

• What are six multiples of 814?

First five multiples of 814 are 1628, 2442, 3256, 4070, 4884, 5698.

• What is prime factorization of 814?

Prime factorization of 814 is 2 x 11 x 37.

• Is 814 a whole number?

Yes 814 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 814? Help her in writing all the factors.

Positive factors are 1, 2, 11, 22, 37, 74, 407, 814.
Negative factors are -1, -2, -11, -22, -37, -74, -407, -814.

Can you help Sammy find out the product of the odd factors of 814?

Factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814.
Odd factors of 814 are 1, 11, 37, 407.
Hence product of odd factors of 814 is; 1 x 11 x 37 x 407 = 165649.

Joey wants to write all the prime factors of 814 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 814 are 2, 11, 37.
So in exponential form it can be written as 2 x 11 x 37.

How many factors are there for 814?

Factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 814. Can you predict the answer?

7 factor(s) of 814 are 1, 2, 11, 22, 37, 74, 407.

Sammy is puzzled while calculating the prime factors of 814. Can you help him find them?

Factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814.
Prime factors of 814 are 2, 11, 37

What is prime factorization of 814?

Prime factorization of 814 is 2 x 11 x 37 = 2 x 11 x 37.