# Factors of 576

Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, and 576

#### How to find factors of a number

 1.   Find factors of 576 using Division Method 2.   Find factors of 576 using Prime Factorization 3.   Find factors of 576 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 576

• Divide 576 by 1: 576 ÷ 1 : Remainder = 0
• Divide 576 by 2: 576 ÷ 2 : Remainder = 0
• Divide 576 by 3: 576 ÷ 3 : Remainder = 0
• Divide 576 by 4: 576 ÷ 4 : Remainder = 0
• Divide 576 by 6: 576 ÷ 6 : Remainder = 0
• Divide 576 by 8: 576 ÷ 8 : Remainder = 0
• Divide 576 by 9: 576 ÷ 9 : Remainder = 0
• Divide 576 by 12: 576 ÷ 12 : Remainder = 0
• Divide 576 by 16: 576 ÷ 16 : Remainder = 0
• Divide 576 by 18: 576 ÷ 18 : Remainder = 0
• Divide 576 by 24: 576 ÷ 24 : Remainder = 0
• Divide 576 by 32: 576 ÷ 32 : Remainder = 0
• Divide 576 by 36: 576 ÷ 36 : Remainder = 0
• Divide 576 by 48: 576 ÷ 48 : Remainder = 0
• Divide 576 by 64: 576 ÷ 64 : Remainder = 0
• Divide 576 by 72: 576 ÷ 72 : Remainder = 0
• Divide 576 by 96: 576 ÷ 96 : Remainder = 0
• Divide 576 by 144: 576 ÷ 144 : Remainder = 0
• Divide 576 by 192: 576 ÷ 192 : Remainder = 0
• Divide 576 by 288: 576 ÷ 288 : Remainder = 0
• Divide 576 by 576: 576 ÷ 576 : Remainder = 0

Hence, Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, and 576

#### 2. Steps to find factors of 576 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 576 using the division method, follow these steps:

• Step 1. Start dividing 576 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 576, which is 2. Divide 576 by 2 to obtain the quotient (288).
576 ÷ 2 = 288
• Step 3. Repeat step 1 with the obtained quotient (288).
288 ÷ 2 = 144
144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 576 is, 576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 576 as shown below:

So, the prime factorization of 576 is, 576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

#### 3. Find factors of 576 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 576 would be the two numbers which, when multiplied, give 576 as the result.

The following table represents the calculation of factors of 576 in pairs:

Factor Pair Pair Factorization
1 and 576 1 x 576 = 576
2 and 288 2 x 288 = 576
3 and 192 3 x 192 = 576
4 and 144 4 x 144 = 576
6 and 96 6 x 96 = 576
8 and 72 8 x 72 = 576
9 and 64 9 x 64 = 576
12 and 48 12 x 48 = 576
16 and 36 16 x 36 = 576
18 and 32 18 x 32 = 576
24 and 24 24 x 24 = 576

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 576. They are called negative pair factors.

Hence, the negative pairs of 576 would be ( -1 , -576 ) , ( -2 , -288 ) , ( -3 , -192 ) , ( -4 , -144 ) , ( -6 , -96 ) , ( -8 , -72 ) , ( -9 , -64 ) , ( -12 , -48 ) , ( -16 , -36 ) , ( -18 , -32 ) and ( -24 , -24 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 576 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 576.
• Every number is a factor of zero (0), since 576 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, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576 are exact divisors of 576.
• Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576. Each factor divides 576 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576 are all less than or equal to 576.

• Which is the smallest prime factor of 576?

Smallest prime factor of 576 is 2.

• Is 576 a perfect square?

Yes 576 is a perfect square.

• What are five multiples of 576?

First five multiples of 576 are 1152, 1728, 2304, 2880, 3456.

• What is prime factorization of 576?

Prime factorization of 576 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

• What are factors of 576?

Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.

• How do you find factors of a negative number? ( eg. -576 )?

Factors of -576 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -144, -192, -288, -576.

• Is 576 a whole number?

Yes 576 is a whole number.

• Which is greatest factor of 576?

The greatest factor of 576 is 288.

• What are the prime factors of 576?

The factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.
Prime factors of 576 are 2, 2, 2, 2, 2, 2, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 576. Can you help her?

Prime factors of 576 are 2, 2, 2, 2, 2, 2, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 576?

Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.
Even factors of 576 are 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.
Hence, product of even factors of 576 is; 2 x 4 x 6 x 8 x 12 x 16 x 18 x 24 x 32 x 36 x 48 x 64 x 72 x 96 x 144 x 192 x 288 x 576 = 3.573323304747203e+27.

Joy wants to calculate mean of all the factors of 576. Help him in finding the mean of 576.

Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 576 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 64 + 72 + 96 + 144 + 192 + 288 + 576 = 1651.
Hence, the mean of factors of 576 is 1651 ÷ 21 = 78.62.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 576? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -144, -192, -288, -576.

How many factors are there for 576?

Factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.
So there are in total 21 factors.

Joey wants to write all the prime factors of 576 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 576 are 2, 2, 2, 2, 2, 2, 3, 3.
So in exponential form it can be written as 26 x 32.

Kevin has been asked to write 20 factor(s) of 576. Can you predict the answer?

20 factor(s) of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288.