# Factors of 564

Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, and 564

#### How to find factors of a number

 1.   Find factors of 564 using Division Method 2.   Find factors of 564 using Prime Factorization 3.   Find factors of 564 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 564

• Divide 564 by 1: 564 ÷ 1 : Remainder = 0
• Divide 564 by 2: 564 ÷ 2 : Remainder = 0
• Divide 564 by 3: 564 ÷ 3 : Remainder = 0
• Divide 564 by 4: 564 ÷ 4 : Remainder = 0
• Divide 564 by 6: 564 ÷ 6 : Remainder = 0
• Divide 564 by 12: 564 ÷ 12 : Remainder = 0
• Divide 564 by 47: 564 ÷ 47 : Remainder = 0
• Divide 564 by 94: 564 ÷ 94 : Remainder = 0
• Divide 564 by 141: 564 ÷ 141 : Remainder = 0
• Divide 564 by 188: 564 ÷ 188 : Remainder = 0
• Divide 564 by 282: 564 ÷ 282 : Remainder = 0
• Divide 564 by 564: 564 ÷ 564 : Remainder = 0

Hence, Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, and 564

#### 2. Steps to find factors of 564 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 564 using the division method, follow these steps:

• Step 1. Start dividing 564 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 564, which is 2. Divide 564 by 2 to obtain the quotient (282).
564 ÷ 2 = 282
• Step 3. Repeat step 1 with the obtained quotient (282).
282 ÷ 2 = 141
141 ÷ 3 = 47
47 ÷ 47 = 1

So, the prime factorization of 564 is, 564 = 2 x 2 x 3 x 47.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 564 as shown below:

So, the prime factorization of 564 is, 564 = 2 x 2 x 3 x 47.

#### 3. Find factors of 564 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 564 would be the two numbers which, when multiplied, give 564 as the result.

The following table represents the calculation of factors of 564 in pairs:

Factor Pair Pair Factorization
1 and 564 1 x 564 = 564
2 and 282 2 x 282 = 564
3 and 188 3 x 188 = 564
4 and 141 4 x 141 = 564
6 and 94 6 x 94 = 564
12 and 47 12 x 47 = 564

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 564. They are called negative pair factors.

Hence, the negative pairs of 564 would be ( -1 , -564 ) , ( -2 , -282 ) , ( -3 , -188 ) , ( -4 , -141 ) , ( -6 , -94 ) and ( -12 , -47 ) .

#### 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. 564 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 564.
• Every number is a factor of zero (0), since 564 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, 12, 47, 94, 141, 188, 282, 564 are exact divisors of 564.
• Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564. Each factor divides 564 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564 are all less than or equal to 564.

• How do you find factors of a negative number? ( eg. -564 )?

Factors of -564 are -1, -2, -3, -4, -6, -12, -47, -94, -141, -188, -282, -564.

• What is the sum of all factors of 564?

The sum of all factors of 564 is 1344.

• What is prime factorization of 564?

Prime factorization of 564 is 2 x 2 x 3 x 47.

• What are the pair factors of 564?

Pair factors of 564 are (1,564), (2,282), (3,188), (4,141), (6,94), (12,47).

• What are six multiples of 564?

First five multiples of 564 are 1128, 1692, 2256, 2820, 3384, 3948.

• Is 564 a whole number?

Yes 564 is a whole number.

• Which is the smallest prime factor of 564?

Smallest prime factor of 564 is 2.

• What are five multiples of 564?

First five multiples of 564 are 1128, 1692, 2256, 2820, 3384.

• Write all factors of 564?

Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.

#### Examples of Factors

Joey wants to write all the prime factors of 564 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 564 are 2, 2, 3, 47.
So in exponential form it can be written as 22 x 3 x 47.

How many factors are there for 564?

Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 564. Can you predict the answer?

11 factor(s) of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282.

Sammy is puzzled while calculating the prime factors of 564. Can you help him find them?

Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.
Prime factors of 564 are 2, 2, 3, 47

What is prime factorization of 564?

Prime factorization of 564 is 2 x 2 x 3 x 47 = 22 x 3 x 47.

Ariel has been assigned the task to find the product of all the prime factors of 564. Can you help her?

Prime factors of 564 are 2, 2, 3, 47.
Hence, the product of prime factors of 282.

Can you help Rubel to find out the product of the even factors of 564?

Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.
Even factors of 564 are 2, 4, 6, 12, 94, 188, 282, 564.
Hence, product of even factors of 564 is; 2 x 4 x 6 x 12 x 94 x 188 x 282 x 564 = 1618961043456.