# Factors of 72

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

#### How to find factors of a number

 1.   Find factors of 72 using Division Method 2.   Find factors of 72 using Prime Factorization 3.   Find factors of 72 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 72

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

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

#### 2. Steps to find factors of 72 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 72 using the division method, follow these steps:

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

So, the prime factorization of 72 is, 72 = 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 72 as shown below:

So, the prime factorization of 72 is, 72 = 2 x 2 x 2 x 3 x 3.

#### 3. Find factors of 72 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 72 would be the two numbers which, when multiplied, give 72 as the result.

The following table represents the calculation of factors of 72 in pairs:

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

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 72. They are called negative pair factors.

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

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

• Which is the smallest prime factor of 72?

Smallest prime factor of 72 is 2.

• Is 72 a perfect square?

No 72 is not a perfect square.

• What are five multiples of 72?

First five multiples of 72 are 144, 216, 288, 360, 432.

• What is prime factorization of 72?

Prime factorization of 72 is 2 x 2 x 2 x 3 x 3.

• What are factors of 72?

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

• How do you find factors of a negative number? ( eg. -72 )?

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

• Is 72 a whole number?

Yes 72 is a whole number.

• Which is greatest factor of 72?

The greatest factor of 72 is 36.

• What are the prime factors of 72?

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Prime factors of 72 are 2, 2, 2, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 72. Can you help her?

Prime factors of 72 are 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 72?

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Even factors of 72 are 2, 4, 6, 8, 12, 18, 24, 36, 72.
Hence, product of even factors of 72 is; 2 x 4 x 6 x 8 x 12 x 18 x 24 x 36 x 72 = 5159780352.

Joy wants to calculate mean of all the factors of 72. Help him in finding the mean of 72.

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 72 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72 = 195.
Hence, the mean of factors of 72 is 195 ÷ 12 = 16.25.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 72? Help her in writing all the factors.

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

How many factors are there for 72?

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

Joey wants to write all the prime factors of 72 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 72 are 2, 2, 2, 3, 3.
So in exponential form it can be written as 23 x 32.

Kevin has been asked to write 11 factor(s) of 72. Can you predict the answer?

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