Factors

# What are the Factors of 48? | Prime Factorization of 48, Factor Tree of 48

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What are the Factors of 48? | Prime Factorization of 48, Factor Tree of 48

**Factors of 48: **There are a total of 10 factors for the number 48. The list of numbers that divides the original number evenly is known as its factors. In the case of 48, the numbers 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 divide the number 48 evenly. **Hence, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.**

The **factors** of a number can be both positive and negative. You can also determine the pair factors of a number. Pair factors are the set of two factors’ whole multiplications in pairs that gives the required number in this case 48). In this article, we will cover:

**How to find factors of 48****Pair factors of 48****Factors of 48 through division method****Factors of 48 through prime factorization Method****Factor tree of 48****Patterns in Factors of 48****Solved examples on factors of 48**

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**What Are the Factors of 48?**

The factors of 48 are the numbers that divide the number (48) evenly without leaving any remainder. The factors of a number can be both positive and negative. Hence, the number 48 has both positive and negative factors.

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

Negative Factors of 48: -1, -2, -3, -4, -6, -8, -12, -16, -24, and -48 |

Prime Factorization of 48: 2 X 2 X 2 X 2 X 3 or 2^{4} X 3 |

Pair Factors of 48: (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8) |

Prime Factors of 48: 2 and 3 |

Sum of Factors of 48: 124 |

Sum of Prime Factors of 48: 5 |

**What Are the Factors of 48 in Pairs?**

A pair factor of 48 is a combination of two numbers, which when multiplied together gives the product of the original number (48). These pair factors are also written in positive and negative pairs as shown in the table below:

**Positive Pair Factors of 48**

The positive pair factors of 48 are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).

**Negative Pair Factors of 48**

The negative pair factors of 48 are (-1, -48), (-2, -24), (-3, -16), (-4, -12), and (-6, -8).

**How To Find Factors of 48 Through Division Method?**

You can determine the factors of 48, using the division method. This approach requires you to multiply a sequence of natural integers by 48. The numbers that divide the 48 completely without leaving any remainder are known as 48 factors. The detailed steps for finding factors of 48 using the division method are as below:

- 48 ÷ 1 = 48
- 48 ÷ 2 = 24
- 48 ÷ 3 = 16
- 48 ÷ 4 = 12
- 48 ÷ 6 = 8
- 48 ÷ 8 = 6
- 48 ÷ 12 = 4
- 48 ÷ 16 = 3
- 48 ÷ 24 =2
- 48 ÷ 48 = 1

Therefore, we can see that 1, 2, 3, 4, 6, 12, 16, 24, and 48 are the numbers that do not leave any remainder when divided by 48. Hence, the factors of 48 are 1, 2, 3, 4, 6, 12, 16, 24, and 48.

**What Is the Prime Factorisation of 48?**

For finding the prime factorization of a number, we need to check if the given number is a prime number. If the given number is a prime number, then it has only two factors: 1 and the number itself. If the given number is a composite number, then it has more than two factors.

Since 48 is the composite number, we have more than two factors. Hence, we can use the prime factorization method to find the factors of 48.

The steps to find prime factors of 48 using the prime factorization method are given below:

**Step 1:**Divide the number 48 by the smallest prime number that is divisible by 48. Hence the smallest prime number that is divisible by 48 is 2.- 48 ÷ 2 = 24

**Step 2:**Now, divide the number 24 (quotient) by the smallest prime number which is 2.- 24 ÷ 2 = 12

**Step 3:**Divide the quotient by 2 repeatedly until you get the number prime number as the quotient.- 12 ÷ 2 = 6
- 6 ÷ 2 = 3

**Step 4:**Now we got 3 as the quotient. Dividing 3 with 3 gives us 1.- 3 ÷ 3 = 1

The quotient is 1. Since 1 cannot be divided further, the **prime factors of 48 are 2 X 2 X 2 X 2 X 3 or 2 ^{4} X 3**. We can also write it down as 2 and 3, as both of them are prime numbers.

The prime factorization for 48 can be represented below:

**What is the Factor Tree of 48?**

Students can also use the factor tree to find the prime factors of 48. In this method, we will place the number 48 at the top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (48). Now, again, we will split the pair of factors into factors. This process will be continued until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 48.

**Step 1:**Let’s place the number 48 at the top of the factor tree and write down 48 in pairs, that is, 2 and 24.**Step 2:**Since 2 is a prime number, we can no longer separate it. We will now divide 24 into 2 and 12.**Step 3:**As we can see, 2 is a prime number but 12 is not, so we will split 12 into 1 and 6.**Step 4:**Now again, we will leave 2 as it is because it is a prime number, but we will break 6 into 2 and 3.**Step 5:**We can see that 2 and 3 are both prime numbers. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches,** 2 ^{4} X 3 or 2 X 2 X 2 X 2 X 3= 48**, which are 48 prime factors.

There are many ways in which we can write the factor tree of 48. Below is an image representation of the factor tree of 48, choosing 6 and 8 as pair factors of 48.

**Factors of 48 Pattern**

The pattern that we observe from the factors of 48 is explained below:

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

From the above, it is clear that the alternative number is doubling.

1, 2, 4, 8, 16

3, 6, 12, 24, 48

Also, the pattern of 48 prime factorizations is as follows:

2

3

2, 2

2, 3

2, 2, 2

2, 2, 3

2, 2, 2, 2

2, 2, 2, 3

2, 2, 2, 2, 3

**Solved Examples on Factors of 48**

Here are some solved examples of 48 factors:

**Q 1: What is the sum of all the factors of 48?A 1: **1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 are the 48 factors.

1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 124

Hence, 124 is the sum of all 48 factors.

**Q 2: What are the factors and prime factors of 48?A 2:** The 48 factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The 48 prime factors are 24 X 3 or 2 X 2 X 2 X 2 X 3.

**Q 3: What’s the highest common factor between 60 and 48?A 3:** The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

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

Hence, from the above, the common factors of 60 and 48 is 1, 2, 3, 4, and 12.

The highest common factor between 60 and 48 is 12.

**Q 4: What’s the highest common factor between 36 and 48?A 4: **The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

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

Hence, from the above, the common factors of 36 and 48 are 1, 2, 3, 4, 6, and 12.

The highest common factor between 36 and 48 is 12.

**Q 5: Is 24 a factor of 48?A 5: **Yes, 24 is a factor of 48.

As 48 ÷ 2 = 24.

**Q 6: What are the factors of -48?A 6: **The factors of -48 are -1, -2, -3, -4, -6, -8, -12, -16, -24, and -48.

**Q 7: What are the common factors of 48 and 54?A 7:** To find the common factors of 48, we need to find the factors of both 48 and 54.

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

Factors of 54: 1, 2, 3, 6, 9, 18, 27 and 54

Hence the common factors of 48 and 54 are 1, 2, 3, and 6.

**Q 8: What are all the factors of 48?A 8: **The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

**Q 9: What are the factors of 48 that are composite?A 9**: Any number which has more than 2 factors is known as a composite number. The list of number which has more than 2 factors in factors of 48 is 4, 6, 8, 12, 16, 24, and 48.

Hence the factors of 48 that are composite are 4, 6, 8, 12, 16, 24, and 48.

**Q 10: What factors of 48 are multiples of 4?A 10: **The factors of 48 that are multiples of 4 are 4, 8, 12, 16, 24, and 48.

4 x 1 = 4

4 x 2 = 8

4 x 3 = 12

4 x 4 = 16

4 x 6 = 24

4 x 12 = 48.

**Q 11: How many 48 factors are odd?A 11: **A total of 2 odd numbers are there in factors of 48 and they are 1 and 3.

**Q 12: What are the factors of 448 that add up to 48?A 12:** The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.

From the above, we can choose 16 and 32.

Adding 16 + 32 = 48

Hence the factors of 448 that add up to 48 are 16 and 32.

**Q 12: What are the factors of 32 and 48?A 12: **The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The factors of 32 are 1, 2, 4, 8, 16, 32, and 64.

**Q 13: What are the common factors of 40 and 48?A 13: **To list out the common factors of 40 and 48, we need to find the factors of both 40 and 48.

Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40

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

From the above, the common factors of 40 and 48 are 1, 2, 4, and 8.

**Q 14: How many different factors are there for the number 48?A 14:** A total of 10 factors are there for the number 48 and they are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

**Q 15: What are the common factors of 48 and 36?A 15: **Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Factors of 36: 2, 3, 4, 6, 9, 12, and 18.

Hence, the common factors of 48 and 36 are 2, 3, 6, and 12.

**Q 16: How many pair factors are there in 48?A 16: **A total of 5 pairs are there in factors of 48.

**Q 17: What is the largest factor of 48?A 17: **The largest factor of 48 is 48.

The second largest factor of 48 is 24.

**Q 18: What patterns do you observe in factors of 48?A 18: **Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

From above, we can see that the alternative number is doubling,

1, 2, 4, 8, 16

3, 6, 12, 24, 48.

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**FAQs on Factors of 48**

**List all the factors of 48**

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

**What are the composite factors of 48?**

**4,**

**6,**8,

**12,**16, 24, and 29 are the 48 composite factors. Composite factors are those that have more than 2 factors other than 1 and itself.

**What are the factors of 48 in pairs?**

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

**What are the positive factors for 48?**

1, 2, 3, 4, 6, 8, 12, 16, 24, and 28 are the positive factors for 48.

**What are the prime factors of 48?**

Prime factors of 48 are 2 and 3.

**What are the factors of 48 that add up to 14?**

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

6 + 8 = 14

Hence, 6 and 8, which are the factors of 48, add up to give 14 as their sum.

**What multiples of 4 are not factors of 48?**

Multiples of 4: 4, 8, 12, 26, 20, 24, 28, 32, 36, 40, and 44.

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

Multiples of 4 are not factors of 48 are 20, 28, 32, 36, 40, 44, and the multiples of 4 that are greater than the number of 48.

**What are the factors of 48 and 72?**

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

Factors of 72: 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

**What are the common factors of 36 and 48?**

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

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

Hence, the common factors of 36 and 48 are 1, 2, 3, 4, 6, and 12.

**What are the common factors of 60, 36, and 48?**

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

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

Hence, the common factors of 60, 36, and 48 are 1, 2, 3, 4, 6, and 12.

Now that you have all the necessary information regarding the factors of 48, We hope this blog has been useful for you and easy to understand as well.

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Written by by

Prerit Jain