# Factors of 2304

Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, and 2304

#### How to find factors of a number

 1.   Find factors of 2304 using Division Method 2.   Find factors of 2304 using Prime Factorization 3.   Find factors of 2304 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2304

• Divide 2304 by 1: 2304 ÷ 1 : Remainder = 0
• Divide 2304 by 2: 2304 ÷ 2 : Remainder = 0
• Divide 2304 by 3: 2304 ÷ 3 : Remainder = 0
• Divide 2304 by 4: 2304 ÷ 4 : Remainder = 0
• Divide 2304 by 6: 2304 ÷ 6 : Remainder = 0
• Divide 2304 by 8: 2304 ÷ 8 : Remainder = 0
• Divide 2304 by 9: 2304 ÷ 9 : Remainder = 0
• Divide 2304 by 12: 2304 ÷ 12 : Remainder = 0
• Divide 2304 by 16: 2304 ÷ 16 : Remainder = 0
• Divide 2304 by 18: 2304 ÷ 18 : Remainder = 0
• Divide 2304 by 24: 2304 ÷ 24 : Remainder = 0
• Divide 2304 by 32: 2304 ÷ 32 : Remainder = 0
• Divide 2304 by 36: 2304 ÷ 36 : Remainder = 0
• Divide 2304 by 48: 2304 ÷ 48 : Remainder = 0
• Divide 2304 by 64: 2304 ÷ 64 : Remainder = 0
• Divide 2304 by 72: 2304 ÷ 72 : Remainder = 0
• Divide 2304 by 96: 2304 ÷ 96 : Remainder = 0
• Divide 2304 by 128: 2304 ÷ 128 : Remainder = 0
• Divide 2304 by 144: 2304 ÷ 144 : Remainder = 0
• Divide 2304 by 192: 2304 ÷ 192 : Remainder = 0
• Divide 2304 by 256: 2304 ÷ 256 : Remainder = 0
• Divide 2304 by 288: 2304 ÷ 288 : Remainder = 0
• Divide 2304 by 384: 2304 ÷ 384 : Remainder = 0
• Divide 2304 by 576: 2304 ÷ 576 : Remainder = 0
• Divide 2304 by 768: 2304 ÷ 768 : Remainder = 0
• Divide 2304 by 1152: 2304 ÷ 1152 : Remainder = 0
• Divide 2304 by 2304: 2304 ÷ 2304 : Remainder = 0

Hence, Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, and 2304

#### 2. Steps to find factors of 2304 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 2304 using the division method, follow these steps:

• Step 1. Start dividing 2304 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 2304, which is 2. Divide 2304 by 2 to obtain the quotient (1152).
2304 ÷ 2 = 1152
• Step 3. Repeat step 1 with the obtained quotient (1152).
1152 ÷ 2 = 576
576 ÷ 2 = 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 2304 is, 2304 = 2 x 2 x 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 2304 as shown below:

So, the prime factorization of 2304 is, 2304 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

#### 3. Find factors of 2304 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 2304 would be the two numbers which, when multiplied, give 2304 as the result.

The following table represents the calculation of factors of 2304 in pairs:

Factor Pair Pair Factorization
1 and 2304 1 x 2304 = 2304
2 and 1152 2 x 1152 = 2304
3 and 768 3 x 768 = 2304
4 and 576 4 x 576 = 2304
6 and 384 6 x 384 = 2304
8 and 288 8 x 288 = 2304
9 and 256 9 x 256 = 2304
12 and 192 12 x 192 = 2304
16 and 144 16 x 144 = 2304
18 and 128 18 x 128 = 2304
24 and 96 24 x 96 = 2304
32 and 72 32 x 72 = 2304
36 and 64 36 x 64 = 2304
48 and 48 48 x 48 = 2304

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 2304. They are called negative pair factors.

Hence, the negative pairs of 2304 would be ( -1 , -2304 ) , ( -2 , -1152 ) , ( -3 , -768 ) , ( -4 , -576 ) , ( -6 , -384 ) , ( -8 , -288 ) , ( -9 , -256 ) , ( -12 , -192 ) , ( -16 , -144 ) , ( -18 , -128 ) , ( -24 , -96 ) , ( -32 , -72 ) , ( -36 , -64 ) and ( -48 , -48 ) .

#### 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. 2304 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 2304.
• Every number is a factor of zero (0), since 2304 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, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304 are exact divisors of 2304.
• Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304. Each factor divides 2304 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, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304 are all less than or equal to 2304.

• Which is the smallest prime factor of 2304?

Smallest prime factor of 2304 is 2.

• Is 2304 a perfect square?

Yes 2304 is a perfect square.

• What are five multiples of 2304?

First five multiples of 2304 are 4608, 6912, 9216, 11520, 13824.

• What is prime factorization of 2304?

Prime factorization of 2304 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

• What are factors of 2304?

Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.

• How do you find factors of a negative number? ( eg. -2304 )?

Factors of -2304 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -128, -144, -192, -256, -288, -384, -576, -768, -1152, -2304.

• Is 2304 a whole number?

Yes 2304 is a whole number.

• Which is greatest factor of 2304?

The greatest factor of 2304 is 1152.

• What are the prime factors of 2304?

The factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.
Prime factors of 2304 are 2, 2, 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 2304. Can you help her?

Prime factors of 2304 are 2, 2, 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 2304?

Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.
Even factors of 2304 are 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.
Hence, product of even factors of 2304 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 128 x 144 x 192 x 256 x 288 x 384 x 576 x 768 x 1152 x 2304 = 9.165362468923399e+43.

Joy wants to calculate mean of all the factors of 2304. Help him in finding the mean of 2304.

Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2304 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 64 + 72 + 96 + 128 + 144 + 192 + 256 + 288 + 384 + 576 + 768 + 1152 + 2304 = 6643.
Hence, the mean of factors of 2304 is 6643 ÷ 27 = 246.04.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2304? 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, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -128, -144, -192, -256, -288, -384, -576, -768, -1152, -2304.

How many factors are there for 2304?

Factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304.
So there are in total 27 factors.

Joey wants to write all the prime factors of 2304 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2304 are 2, 2, 2, 2, 2, 2, 2, 2, 3, 3.
So in exponential form it can be written as 28 x 32.

Kevin has been asked to write 26 factor(s) of 2304. Can you predict the answer?

26 factor(s) of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152.