# Factors of 824

Factors of 824 are 1, 2, 4, 8, 103, 206, 412, and 824

#### How to find factors of a number

 1.   Find factors of 824 using Division Method 2.   Find factors of 824 using Prime Factorization 3.   Find factors of 824 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 824

• Divide 824 by 1: 824 ÷ 1 : Remainder = 0
• Divide 824 by 2: 824 ÷ 2 : Remainder = 0
• Divide 824 by 4: 824 ÷ 4 : Remainder = 0
• Divide 824 by 8: 824 ÷ 8 : Remainder = 0
• Divide 824 by 103: 824 ÷ 103 : Remainder = 0
• Divide 824 by 206: 824 ÷ 206 : Remainder = 0
• Divide 824 by 412: 824 ÷ 412 : Remainder = 0
• Divide 824 by 824: 824 ÷ 824 : Remainder = 0

Hence, Factors of 824 are 1, 2, 4, 8, 103, 206, 412, and 824

#### 2. Steps to find factors of 824 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 824 using the division method, follow these steps:

• Step 1. Start dividing 824 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 824, which is 2. Divide 824 by 2 to obtain the quotient (412).
824 ÷ 2 = 412
• Step 3. Repeat step 1 with the obtained quotient (412).
412 ÷ 2 = 206
206 ÷ 2 = 103
103 ÷ 103 = 1

So, the prime factorization of 824 is, 824 = 2 x 2 x 2 x 103.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 824 as shown below:

So, the prime factorization of 824 is, 824 = 2 x 2 x 2 x 103.

#### 3. Find factors of 824 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 824 would be the two numbers which, when multiplied, give 824 as the result.

The following table represents the calculation of factors of 824 in pairs:

Factor Pair Pair Factorization
1 and 824 1 x 824 = 824
2 and 412 2 x 412 = 824
4 and 206 4 x 206 = 824
8 and 103 8 x 103 = 824

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 824. They are called negative pair factors.

Hence, the negative pairs of 824 would be ( -1 , -824 ) , ( -2 , -412 ) , ( -4 , -206 ) and ( -8 , -103 ) .

#### 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. 824 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 824.
• Every number is a factor of zero (0), since 824 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, 8, 103, 206, 412, 824 are exact divisors of 824.
• Factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824. Each factor divides 824 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 103, 206, 412, 824 are all less than or equal to 824.

• What are the pair factors of 824?

Pair factors of 824 are (1,824), (2,412), (4,206), (8,103).

• What are five multiples of 824?

First five multiples of 824 are 1648, 2472, 3296, 4120, 4944.

• What two numbers make 824?

Two numbers that make 824 are 2 and 412.

• What is the sum of all factors of 824?

The sum of all factors of 824 is 1560.

• What are factors of -824?

Factors of -824 are -1, -2, -4, -8, -103, -206, -412, -824.

• What are factors of 824?

Factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824.

• Is 824 a perfect square?

No 824 is not a perfect square.

• Which is the smallest prime factor of 824?

Smallest prime factor of 824 is 2.

• Which is greatest factor of 824?

The greatest factor of 824 is 412.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 824?

Factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824.
Odd factors of 824 are 1, 103.
Hence product of odd factors of 824 is; 1 x 103 = 103.

Joey wants to write all the prime factors of 824 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 824 are 2, 2, 2, 103.
So in exponential form it can be written as 23 x 103.

How many factors are there for 824?

Factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 824. Can you predict the answer?

7 factor(s) of 824 are 1, 2, 4, 8, 103, 206, 412.

Sammy is puzzled while calculating the prime factors of 824. Can you help him find them?

Factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824.
Prime factors of 824 are 2, 2, 2, 103

What is prime factorization of 824?

Prime factorization of 824 is 2 x 2 x 2 x 103 = 23 x 103.

Can you help Rubel to find out the product of the even factors of 824?

Factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824.
Even factors of 824 are 2, 4, 8, 206, 412, 824.
Hence, product of even factors of 824 is; 2 x 4 x 8 x 206 x 412 x 824 = 4475809792.