# Factors of 828

Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828

#### How to find factors of a number

 1.   Find factors of 828 using Division Method 2.   Find factors of 828 using Prime Factorization 3.   Find factors of 828 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 828

• Divide 828 by 1: 828 ÷ 1 : Remainder = 0
• Divide 828 by 2: 828 ÷ 2 : Remainder = 0
• Divide 828 by 3: 828 ÷ 3 : Remainder = 0
• Divide 828 by 4: 828 ÷ 4 : Remainder = 0
• Divide 828 by 6: 828 ÷ 6 : Remainder = 0
• Divide 828 by 9: 828 ÷ 9 : Remainder = 0
• Divide 828 by 12: 828 ÷ 12 : Remainder = 0
• Divide 828 by 18: 828 ÷ 18 : Remainder = 0
• Divide 828 by 23: 828 ÷ 23 : Remainder = 0
• Divide 828 by 36: 828 ÷ 36 : Remainder = 0
• Divide 828 by 46: 828 ÷ 46 : Remainder = 0
• Divide 828 by 69: 828 ÷ 69 : Remainder = 0
• Divide 828 by 92: 828 ÷ 92 : Remainder = 0
• Divide 828 by 138: 828 ÷ 138 : Remainder = 0
• Divide 828 by 207: 828 ÷ 207 : Remainder = 0
• Divide 828 by 276: 828 ÷ 276 : Remainder = 0
• Divide 828 by 414: 828 ÷ 414 : Remainder = 0
• Divide 828 by 828: 828 ÷ 828 : Remainder = 0

Hence, Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828

#### 2. Steps to find factors of 828 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 828 using the division method, follow these steps:

• Step 1. Start dividing 828 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 828, which is 2. Divide 828 by 2 to obtain the quotient (414).
828 ÷ 2 = 414
• Step 3. Repeat step 1 with the obtained quotient (414).
414 ÷ 2 = 207
207 ÷ 3 = 69
69 ÷ 3 = 23
23 ÷ 23 = 1

So, the prime factorization of 828 is, 828 = 2 x 2 x 3 x 3 x 23.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 828 as shown below:

So, the prime factorization of 828 is, 828 = 2 x 2 x 3 x 3 x 23.

#### 3. Find factors of 828 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 828 would be the two numbers which, when multiplied, give 828 as the result.

The following table represents the calculation of factors of 828 in pairs:

Factor Pair Pair Factorization
1 and 828 1 x 828 = 828
2 and 414 2 x 414 = 828
3 and 276 3 x 276 = 828
4 and 207 4 x 207 = 828
6 and 138 6 x 138 = 828
9 and 92 9 x 92 = 828
12 and 69 12 x 69 = 828
18 and 46 18 x 46 = 828
23 and 36 23 x 36 = 828

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 828. They are called negative pair factors.

Hence, the negative pairs of 828 would be ( -1 , -828 ) , ( -2 , -414 ) , ( -3 , -276 ) , ( -4 , -207 ) , ( -6 , -138 ) , ( -9 , -92 ) , ( -12 , -69 ) , ( -18 , -46 ) and ( -23 , -36 ) .

#### 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. 828 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 828.
• Every number is a factor of zero (0), since 828 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, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 are exact divisors of 828.
• Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. Each factor divides 828 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 are all less than or equal to 828.

• Which is the smallest prime factor of 828?

Smallest prime factor of 828 is 2.

• Is 828 a perfect square?

No 828 is not a perfect square.

• What are five multiples of 828?

First five multiples of 828 are 1656, 2484, 3312, 4140, 4968.

• What is prime factorization of 828?

Prime factorization of 828 is 2 x 2 x 3 x 3 x 23.

• What are factors of 828?

Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.

• How do you find factors of a negative number? ( eg. -828 )?

Factors of -828 are -1, -2, -3, -4, -6, -9, -12, -18, -23, -36, -46, -69, -92, -138, -207, -276, -414, -828.

• Is 828 a whole number?

Yes 828 is a whole number.

• Which is greatest factor of 828?

The greatest factor of 828 is 414.

• What are the prime factors of 828?

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
Prime factors of 828 are 2, 2, 3, 3, 23.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 828. Can you help her?

Prime factors of 828 are 2, 2, 3, 3, 23.
Hence, the product of prime factors of 138.

Can you help Rubel to find out the product of the even factors of 828?

Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
Even factors of 828 are 2, 4, 6, 12, 18, 36, 46, 92, 138, 276, 414, 828.
Hence, product of even factors of 828 is; 2 x 4 x 6 x 12 x 18 x 36 x 46 x 92 x 138 x 276 x 414 x 828 = 20623482129232430000.

Joy wants to calculate mean of all the factors of 828. Help him in finding the mean of 828.

Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 828 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 23 + 36 + 46 + 69 + 92 + 138 + 207 + 276 + 414 + 828 = 2184.
Hence, the mean of factors of 828 is 2184 ÷ 18 = 121.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 828? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
Negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -23, -36, -46, -69, -92, -138, -207, -276, -414, -828.

How many factors are there for 828?

Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
So there are in total 18 factors.

Joey wants to write all the prime factors of 828 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 828 are 2, 2, 3, 3, 23.
So in exponential form it can be written as 22 x 32 x 23.

Kevin has been asked to write 17 factor(s) of 828. Can you predict the answer?

17 factor(s) of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414.