# Factors of 567

Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, and 567

#### How to find factors of a number

 1.   Find factors of 567 using Division Method 2.   Find factors of 567 using Prime Factorization 3.   Find factors of 567 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 567

• Divide 567 by 1: 567 ÷ 1 : Remainder = 0
• Divide 567 by 3: 567 ÷ 3 : Remainder = 0
• Divide 567 by 7: 567 ÷ 7 : Remainder = 0
• Divide 567 by 9: 567 ÷ 9 : Remainder = 0
• Divide 567 by 21: 567 ÷ 21 : Remainder = 0
• Divide 567 by 27: 567 ÷ 27 : Remainder = 0
• Divide 567 by 63: 567 ÷ 63 : Remainder = 0
• Divide 567 by 81: 567 ÷ 81 : Remainder = 0
• Divide 567 by 189: 567 ÷ 189 : Remainder = 0
• Divide 567 by 567: 567 ÷ 567 : Remainder = 0

Hence, Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, and 567

#### 2. Steps to find factors of 567 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 567 using the division method, follow these steps:

• Step 1. Start dividing 567 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 567, which is 3. Divide 567 by 3 to obtain the quotient (189).
567 ÷ 3 = 189
• Step 3. Repeat step 1 with the obtained quotient (189).
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So, the prime factorization of 567 is, 567 = 3 x 3 x 3 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 567 as shown below:

So, the prime factorization of 567 is, 567 = 3 x 3 x 3 x 3 x 7.

#### 3. Find factors of 567 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 567 would be the two numbers which, when multiplied, give 567 as the result.

The following table represents the calculation of factors of 567 in pairs:

Factor Pair Pair Factorization
1 and 567 1 x 567 = 567
3 and 189 3 x 189 = 567
7 and 81 7 x 81 = 567
9 and 63 9 x 63 = 567
21 and 27 21 x 27 = 567

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 567. They are called negative pair factors.

Hence, the negative pairs of 567 would be ( -1 , -567 ) , ( -3 , -189 ) , ( -7 , -81 ) , ( -9 , -63 ) and ( -21 , -27 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 567 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, 3, 7, 9, 21, 27, 63, 81, 189, 567 are exact divisors of 567.
• Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567. Each factor divides 567 without leaving a remainder.

• Which is the smallest prime factor of 567?

Smallest prime factor of 567 is 3.

• Is 567 a perfect square?

No 567 is not a perfect square.

• What are five multiples of 567?

First five multiples of 567 are 1134, 1701, 2268, 2835, 3402.

• What is prime factorization of 567?

Prime factorization of 567 is 3 x 3 x 3 x 3 x 7.

• What are factors of 567?

Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.

• How do you find factors of a negative number? ( eg. -567 )?

Factors of -567 are -1, -3, -7, -9, -21, -27, -63, -81, -189, -567.

• Is 567 a whole number?

Yes 567 is a whole number.

• Which is greatest factor of 567?

The greatest factor of 567 is 189.

• What are the prime factors of 567?

The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.
Prime factors of 567 are 3, 3, 3, 3, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 567. Can you help her?

Prime factors of 567 are 3, 3, 3, 3, 7.
Hence, the product of prime factors of 21.

Can you help Rubel to find out the product of the even factors of 567?

Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.
Even factors of 567 are 0.
Hence, product of even factors of 567 is; 0 = 0.

Joy wants to calculate mean of all the factors of 567. Help him in finding the mean of 567.

Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 567 is 1 + 3 + 7 + 9 + 21 + 27 + 63 + 81 + 189 + 567 = 968.
Hence, the mean of factors of 567 is 968 ÷ 10 = 96.80.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 567? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.
Negative factors are -1, -3, -7, -9, -21, -27, -63, -81, -189, -567.

How many factors are there for 567?

Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.
So there are in total 10 factors.

Joey wants to write all the prime factors of 567 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 567 are 3, 3, 3, 3, 7.
So in exponential form it can be written as 34 x 7.

Kevin has been asked to write 9 factor(s) of 567. Can you predict the answer?

9 factor(s) of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189.