# Factors of 825

Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825

#### How to find factors of a number

 1.   Find factors of 825 using Division Method 2.   Find factors of 825 using Prime Factorization 3.   Find factors of 825 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 825

• Divide 825 by 1: 825 ÷ 1 : Remainder = 0
• Divide 825 by 3: 825 ÷ 3 : Remainder = 0
• Divide 825 by 5: 825 ÷ 5 : Remainder = 0
• Divide 825 by 11: 825 ÷ 11 : Remainder = 0
• Divide 825 by 15: 825 ÷ 15 : Remainder = 0
• Divide 825 by 25: 825 ÷ 25 : Remainder = 0
• Divide 825 by 33: 825 ÷ 33 : Remainder = 0
• Divide 825 by 55: 825 ÷ 55 : Remainder = 0
• Divide 825 by 75: 825 ÷ 75 : Remainder = 0
• Divide 825 by 165: 825 ÷ 165 : Remainder = 0
• Divide 825 by 275: 825 ÷ 275 : Remainder = 0
• Divide 825 by 825: 825 ÷ 825 : Remainder = 0

Hence, Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825

#### 2. Steps to find factors of 825 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 825 using the division method, follow these steps:

• Step 1. Start dividing 825 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 825, which is 3. Divide 825 by 3 to obtain the quotient (275).
825 ÷ 3 = 275
• Step 3. Repeat step 1 with the obtained quotient (275).
275 ÷ 5 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1

So, the prime factorization of 825 is, 825 = 3 x 5 x 5 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 825 as shown below:

So, the prime factorization of 825 is, 825 = 3 x 5 x 5 x 11.

#### 3. Find factors of 825 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 825 would be the two numbers which, when multiplied, give 825 as the result.

The following table represents the calculation of factors of 825 in pairs:

Factor Pair Pair Factorization
1 and 825 1 x 825 = 825
3 and 275 3 x 275 = 825
5 and 165 5 x 165 = 825
11 and 75 11 x 75 = 825
15 and 55 15 x 55 = 825
25 and 33 25 x 33 = 825

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 825. They are called negative pair factors.

Hence, the negative pairs of 825 would be ( -1 , -825 ) , ( -3 , -275 ) , ( -5 , -165 ) , ( -11 , -75 ) , ( -15 , -55 ) and ( -25 , -33 ) .

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825 are exact divisors of 825.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 825 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 825.

• How do you find factors of a negative number? ( eg. -825 )?

Factors of -825 are -1, -3, -5, -11, -15, -25, -33, -55, -75, -165, -275, -825.

• What is the sum of all factors of 825?

The sum of all factors of 825 is 1488.

• What is prime factorization of 825?

Prime factorization of 825 is 3 x 5 x 5 x 11.

• What are the pair factors of 825?

Pair factors of 825 are (1,825), (3,275), (5,165), (11,75), (15,55), (25,33).

• What are six multiples of 825?

First five multiples of 825 are 1650, 2475, 3300, 4125, 4950, 5775.

• Is 825 a whole number?

Yes 825 is a whole number.

• Which is the smallest prime factor of 825?

Smallest prime factor of 825 is 3.

• What are five multiples of 825?

First five multiples of 825 are 1650, 2475, 3300, 4125, 4950.

• Write all factors of 825?

Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.

#### Examples of Factors

Joey wants to write all the prime factors of 825 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 825 are 3, 5, 5, 11.
So in exponential form it can be written as 3 x 52 x 11.

How many factors are there for 825?

Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 825. Can you predict the answer?

11 factor(s) of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275.

Sammy is puzzled while calculating the prime factors of 825. Can you help him find them?

Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.
Prime factors of 825 are 3, 5, 5, 11

What is prime factorization of 825?

Prime factorization of 825 is 3 x 5 x 5 x 11 = 3 x 52 x 11.

Ariel has been assigned the task to find the product of all the prime factors of 825. Can you help her?

Prime factors of 825 are 3, 5, 5, 11.
Hence, the product of prime factors of 165.

Can you help Rubel to find out the product of the even factors of 825?

Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.
Even factors of 825 are 0.
Hence, product of even factors of 825 is; 0 = 0.