# Factors of 48

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

#### How to find factors of a number

 1.   Find factors of 48 using Division Method 2.   Find factors of 48 using Prime Factorization 3.   Find factors of 48 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 48

• Divide 48 by 1: 48 ÷ 1 : Remainder = 0
• Divide 48 by 2: 48 ÷ 2 : Remainder = 0
• Divide 48 by 3: 48 ÷ 3 : Remainder = 0
• Divide 48 by 4: 48 ÷ 4 : Remainder = 0
• Divide 48 by 6: 48 ÷ 6 : Remainder = 0
• Divide 48 by 8: 48 ÷ 8 : Remainder = 0
• Divide 48 by 12: 48 ÷ 12 : Remainder = 0
• Divide 48 by 16: 48 ÷ 16 : Remainder = 0
• Divide 48 by 24: 48 ÷ 24 : Remainder = 0
• Divide 48 by 48: 48 ÷ 48 : Remainder = 0

Hence, Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

#### 2. Steps to find factors of 48 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 48 using the division method, follow these steps:

• Step 1. Start dividing 48 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 48, which is 2. Divide 48 by 2 to obtain the quotient (24).
48 ÷ 2 = 24
• Step 3. Repeat step 1 with the obtained quotient (24).
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1

So, the prime factorization of 48 is, 48 = 2 x 2 x 2 x 2 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 48 as shown below:

So, the prime factorization of 48 is, 48 = 2 x 2 x 2 x 2 x 3.

#### 3. Find factors of 48 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 48 would be the two numbers which, when multiplied, give 48 as the result.

The following table represents the calculation of factors of 48 in pairs:

Factor Pair Pair Factorization
1 and 48 1 x 48 = 48
2 and 24 2 x 24 = 48
3 and 16 3 x 16 = 48
4 and 12 4 x 12 = 48
6 and 8 6 x 8 = 48

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 48. They are called negative pair factors.

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

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

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

• What are the prime factors of 48?

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Prime factors of 48 are 2, 2, 2, 2, 3.

• What two numbers make 48?

Two numbers that make 48 are 2 and 24.

• What is the greatest prime factors of 48?

The greatest prime factor of 48 is 3.

• What are factors of 48?

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

• How do you find factors of a negative number? ( eg. -48 )?

Factors of -48 are -1, -2, -3, -4, -6, -8, -12, -16, -24, -48.

• What are five multiples of 48?

First five multiples of 48 are 96, 144, 192, 240, 288.

• Write some multiples of 48?

First five multiples of 48 are 96, 144, 192, 240.

• Is 48 a perfect square?

No 48 is not a perfect square.

• What two numbers make 48?

Two numbers that make 48 are 2 and 24.

#### Examples of Factors

What is prime factorization of 48?

Prime factorization of 48 is 2 x 2 x 2 x 2 x 3 = 24 x 3.

Sammy is puzzled while calculating the prime factors of 48. Can you help him find them?

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Prime factors of 48 are 2, 2, 2, 2, 3

Kevin has been asked to write 9 factor(s) of 48. Can you predict the answer?

9 factor(s) of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24.

Joey wants to write all the prime factors of 48 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 48 are 2, 2, 2, 2, 3.
So in exponential form it can be written as 24 x 3.

How many factors are there for 48?

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
So there are in total 10 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 48? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Negative factors are -1, -2, -3, -4, -6, -8, -12, -16, -24, -48.

Can you help Rubel to find out the product of the even factors of 48?

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Even factors of 48 are 2, 4, 6, 8, 12, 16, 24, 48.
Hence, product of even factors of 48 is; 2 x 4 x 6 x 8 x 12 x 16 x 24 x 48 = 84934656.