Factors of 48: Prime Factorization, Pair Factors & Examples

Factors of 48 are the numbers that divide 48 completely without leaving any remainder. There are 10 factors of 48 which are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The numbers that give the original number 48 when multiplied together in pairs are the factors of 48. The pair factors of 48 are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8). Factors of 48 can be both positive and negative. For instance, the factors of 48 can be (1, 48) or (-1, -48). The product of the pair of negative factors will also result in the original number 48. The Prime Factorization of 48 is 2 x 2 x 2 x 2 × 3. There are two prime factors of 48 which are 2 and 3.

Key Terms: Factors of 48, Pair Factors, Prime Factors, Prime Factorization, Composite Number, Factors, Remainder, Integers

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What are the Factors of 48?

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Factors of 48 are those numbers that when multiplied in pairs result in the number 48. The numbers that divide 48 exactly leaving zero as the remainder are the factors of 48. 48 is an even composite number, which means 48 has many factors other than 1 and 48. The factors of 48 are 10 in number which are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

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

Factors of 48

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Pair Factors of 48

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Pair Factors of 48 are those numbers that when multiplied together result in the original number 48. Pair factors of 48 can be negative as well as positive.

Positive Pair Factors of 48

The positive pair factors of 48 are as follows:

Negative Pair Factors of 48

The negative pair factors of 48 are as follows:

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How to Calculate Factors of 48?

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In order to calculate the factors of 48, one needs to follow the given steps:

• Step 1: Write the number whose factors are to be calculated which is 48. 48 is an even composite number that can be factored further.
• Step 2: Now, find the two numbers whose product is 48. 2 × 24 = 48. Here, 2 is a prime number and can not be factored further. 
• Step 3: Since 24 is not prime, break it down into factors. 2 × 12 = 24. Here again, 2 is a prime number.
• Step 4: Now, break 12 into factors. 3 × 4 = 12. Here, 3 is a prime number and can not be factored further.
• Step 5: Breakdown 4 into factors. 2 × 2 = 4. Now both the numbers that are left are 2 which can not be factored further.

It means we have found all the factors of 48. Thus, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

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Factors of 48 by Division Method

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The factors of 48 can be found by dividing 48 by different consecutive integers in the division method. If a number divides 48 completely and leaves the remainder as zero, then the given number is a factor of 48.

• 48÷1 = 48 (Thus, 1 is a factor)
• 48÷2 = 24 (Thus, 2 is a factor)
• 48÷3 = 16 (Thus, 3 is a factor)
• 48÷4 = 12 (Thus, 4 is a factor)
• 48÷6 = 8 (Thus, 6 is a factor)
• 48÷8 =6 (Thus, 8 is a factor)
• 48÷12 = 4 (Thus, 12 is a factor)
• 48÷16 = 3 (Thus, 16 is a factor)
• 48÷24 = 2 (Thus, 24 is a factor)
• 48÷48 = 1 (Thus, 48 is a factor)

Hence, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

On dividing 48 by any other numbers other than 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, there would be a remainder which means that they are not the factors of 48.

Read More: Multiplication and Division of Integers

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Prime Factorization of 48

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Prime Factorization refer to the process of writing a number as a product of its prime factors. Prime Factors are those factors of a number that are prime numbers. 

48 is a composite number, so we can get its factors through prime factorization:

Prime Factorization of 48

Step 1: The given number is 48 which can be factored as a product of 6 and 8.

Step 2: Now, we will check whether each one of them is prime or not.

• 6 is not a prime number and can be factored further as a product of 2 and 3.
• 8 is not a prime number and can be factored further as a product of 2 and 4.
• Now, as 4 is also not a prime number, it can be factored as a product of 2 and 2.

Step 3: 48 can be thus written as

48 = 6 × 8 = 2 × 3 × 2 × 2 × 2

48 = 24 × 31

So the prime factorization of 48 is 2 × 2 × 2 × 2 × 3 which can also be written as 24 × 3. Thus, 2 and 3 are the prime factors of 48.

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Factors of 48 by Factor Tree Method

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The factors of 48 can be represented in the form of the factor tree method as 

Factor Tree of 48

Solved Examples on Factor of 48

Example 1: List the common factors of 48 and 47.

Solution: First, we will write down the factors of 48 and 47.

• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• Factors of 47: 1, 47

Thus, the only common factor of 47 and 48 is 1.

Example 2: What are the common factors of 48 and 49?

Solution: The factors of 48 and 49 are as follows: 

• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• Factors of 49: 1, 7, 49

Hence, there is only 1 common factor of 48 and 49 which is 1.

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Things to Remember

• Factors of 48 are defined as those numbers that divide the number 15 completely without any remainder.
• 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 are the 10 factors of 48.
• The prime factorization of 48 is 2 × 2 × 2 × 2 × 3 = 24 × 3
• The two prime factors of 48 are 2 and 3.
• The sum of all the factors of 48 is 124.