# Factors of 144

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144

#### How to find factors of a number

 1.   Find factors of 144 using Division Method 2.   Find factors of 144 using Prime Factorization 3.   Find factors of 144 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 144

• Divide 144 by 1: 144 ÷ 1 : Remainder = 0
• Divide 144 by 2: 144 ÷ 2 : Remainder = 0
• Divide 144 by 3: 144 ÷ 3 : Remainder = 0
• Divide 144 by 4: 144 ÷ 4 : Remainder = 0
• Divide 144 by 6: 144 ÷ 6 : Remainder = 0
• Divide 144 by 8: 144 ÷ 8 : Remainder = 0
• Divide 144 by 9: 144 ÷ 9 : Remainder = 0
• Divide 144 by 12: 144 ÷ 12 : Remainder = 0
• Divide 144 by 16: 144 ÷ 16 : Remainder = 0
• Divide 144 by 18: 144 ÷ 18 : Remainder = 0
• Divide 144 by 24: 144 ÷ 24 : Remainder = 0
• Divide 144 by 36: 144 ÷ 36 : Remainder = 0
• Divide 144 by 48: 144 ÷ 48 : Remainder = 0
• Divide 144 by 72: 144 ÷ 72 : Remainder = 0
• Divide 144 by 144: 144 ÷ 144 : Remainder = 0

Hence, Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144

#### 2. Steps to find factors of 144 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 144 using the division method, follow these steps:

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

So, the prime factorization of 144 is, 144 = 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 144 as shown below:

So, the prime factorization of 144 is, 144 = 2 x 2 x 2 x 2 x 3 x 3.

#### 3. Find factors of 144 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 144 would be the two numbers which, when multiplied, give 144 as the result.

The following table represents the calculation of factors of 144 in pairs:

Factor Pair Pair Factorization
1 and 144 1 x 144 = 144
2 and 72 2 x 72 = 144
3 and 48 3 x 48 = 144
4 and 36 4 x 36 = 144
6 and 24 6 x 24 = 144
8 and 18 8 x 18 = 144
9 and 16 9 x 16 = 144
12 and 12 12 x 12 = 144

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 144. They are called negative pair factors.

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

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

• Which is the smallest prime factor of 144?

Smallest prime factor of 144 is 2.

• Is 144 a perfect square?

Yes 144 is a perfect square.

• What are five multiples of 144?

First five multiples of 144 are 288, 432, 576, 720, 864.

• What is prime factorization of 144?

Prime factorization of 144 is 2 x 2 x 2 x 2 x 3 x 3.

• What are factors of 144?

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.

• How do you find factors of a negative number? ( eg. -144 )?

Factors of -144 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, -144.

• Is 144 a whole number?

Yes 144 is a whole number.

• Which is greatest factor of 144?

The greatest factor of 144 is 72.

• What are the prime factors of 144?

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Prime factors of 144 are 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 144. Can you help her?

Prime factors of 144 are 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 144?

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Even factors of 144 are 2, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 144.
Hence, product of even factors of 144 is; 2 x 4 x 6 x 8 x 12 x 16 x 18 x 24 x 36 x 48 x 72 x 144 = 570630428688384.

Joy wants to calculate mean of all the factors of 144. Help him in finding the mean of 144.

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 144 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 + 144 = 403.
Hence, the mean of factors of 144 is 403 ÷ 15 = 26.87.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 144? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, -144.

How many factors are there for 144?

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
So there are in total 15 factors.

Joey wants to write all the prime factors of 144 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 144 are 2, 2, 2, 2, 3, 3.
So in exponential form it can be written as 24 x 32.

Kevin has been asked to write 14 factor(s) of 144. Can you predict the answer?

14 factor(s) of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72.