# Factors of 1152

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

#### How to find factors of a number

 1.   Find factors of 1152 using Division Method 2.   Find factors of 1152 using Prime Factorization 3.   Find factors of 1152 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1152

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

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

#### 2. Steps to find factors of 1152 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 1152 using the division method, follow these steps:

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

So, the prime factorization of 1152 is, 1152 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

#### 3. Find factors of 1152 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 1152 would be the two numbers which, when multiplied, give 1152 as the result.

The following table represents the calculation of factors of 1152 in pairs:

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

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 1152. They are called negative pair factors.

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

#### 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

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

• Which is the smallest prime factor of 1152?

Smallest prime factor of 1152 is 2.

• Is 1152 a perfect square?

No 1152 is not a perfect square.

• What are five multiples of 1152?

First five multiples of 1152 are 2304, 3456, 4608, 5760, 6912.

• What is prime factorization of 1152?

Prime factorization of 1152 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

• What are factors of 1152?

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

• How do you find factors of a negative number? ( eg. -1152 )?

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

• Is 1152 a whole number?

Yes 1152 is a whole number.

• Which is greatest factor of 1152?

The greatest factor of 1152 is 576.

• What are the prime factors of 1152?

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

Prime factors of 1152 are 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 1152?

Factors of 1152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152.
Even factors of 1152 are 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152.
Hence, product of even factors of 1152 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 288 x 384 x 576 x 1152 = 2.023326571103246e+35.

Joy wants to calculate mean of all the factors of 1152. Help him in finding the mean of 1152.

Factors of 1152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1152 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 64 + 72 + 96 + 128 + 144 + 192 + 288 + 384 + 576 + 1152 = 3315.
Hence, the mean of factors of 1152 is 3315 ÷ 24 = 138.13.

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

How many factors are there for 1152?

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

Joey wants to write all the prime factors of 1152 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1152 are 2, 2, 2, 2, 2, 2, 2, 3, 3.
So in exponential form it can be written as 27 x 32.

Kevin has been asked to write 23 factor(s) of 1152. Can you predict the answer?

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