Factors

# What are the Factors of 105? | Prime Factorization of 105

Written by Prerit Jain

Updated on: 12 Aug 2023

### What are the Factors of 105? | Prime Factorization of 105

The 105 factors are the numbers that will be divided by 105 exactly without any remainder. These factors can be negative or positive. Moreover, their factor pairs will also be either negative or positive. The factors of 105 are 1, 3, 5, 7, 15, 21, 25, and 105. Let’s learn everything about factors of 105 along with solved examples. Scroll down to find out more.

## What Are the Factors of 105?

Numbers that cannot be divided by 105 exactly without leaving a remainder are known as factors of 105. In short, they a pair of numbers that are multiplied to achieve 105 are known as 105 pair factors. Since 105 is a composite number, it has more than one factor, and the number itself is included.

• 1, 3, 5, 7, 15, 21, 35, and 105 are 105 positive factors.
• -1, -3, -5, -7, -15, -21, -35, and -105 are the 105 negative factors.
• 3 X 5 X 7 is the prime factorization of 105.
• 3, 5, 7 are prime factors of 105.
• The sum of prime factors of 105 are 15
• The sum of factors of 105 are 192.

## Write Factors of 105 in Pairs?

The 105 pair factors are the pair of numbers that provide us with the original 105 numerals after multiplication. As we said, they can either be positive or negative. Below are the positive and negative 105 pair factors:

### Positive Pair Factors of 105

The 105 positive pairs are: (1, 105), (3, 35), (5, 21), (7, 15).

### Negative Pair Factors of 105

The 105 negative pairs are: (-1, -105), (-3, -35), (-5, -21), (-7, -15).

## How To Find Factors of 105 Through Division Method?

You can find 105 factors through the division method. In this method, you will divide every integer from 1 to 105, and the ones that get divided exactly with 0 as the remainder are the factors. Let’s start by dividing them:

• 105 ÷ 1 = 105
• 105 ÷ 3 = 35
• 105 ÷ 5 = 21
• 105 ÷ 7 = 15
• 105 ÷ 15 = 7
• 105 ÷ 21 = 5
• 105 ÷ 35 = 3
• 105 ÷ 105 = 1

Hence, after division, we can see that 1, 3, 5, 7, 15, 21, 35, and 105 are the 105 factors through the division method. Moreover, if we divide it by any number, it will leave a remainder.

## What Is the Prime Factorisation of 105?

We can find prime factors of 105 using the prime factorisation method. The steps to find prime factors of 105 using the prime factorization method are explained below.

• Step 1: Divide 105 by the least prime number that is divisible by 105 without leaving any remainder.
• Step 2: The least prime number is 3, and when 3 is divided by 105, the remainder is 0, and the quotient is 35.
• Step 3: Now divide the number 35 with the least prime number, which doesn’t leave any remainder. Hence, the least prime number chosen here is 5.
• Step 4: Dividing the number 5 with 35 gives 7.
• Step 5: Since 7 itself is a prime number, we cannot divide it further.

Hence, the prime factors of 105 using prime factorization are 3 X 5 X 7.

## Write the Factor Tree of 105

You can also use the factor tree method to find prime numbers under 105. Below are the steps on how to find the factor tree of 105:

• Step 1: Firstly, we will write 105 at the top of the factor tree and then write 3 and 35.
• Step 2: Since 3 is a prime number, we cannot factorise it further. So, we will circle 3.
• Step 3: Now, we will split 35 into 5 and 7. Let’s take a look and see if they are prime numbers or not.

Both of them are prime numbers, so we will circle them. Hence, the prime factors of 105 using the factor tree are 3, 5, and 7.

## Solved Examples on Factors of 105

What is the sum of all the factors of 105?
1, 3, 5, 7, 15, 21, 35, and 105 are the 105 factors.
1 + 3 + 5 + 7 + 15 + 21 + 35 + 105 = 192
Hence, 192 is the sum of all 105 factors.

What are the factors and prime factors of 105?
The 105 factors are: 1, 3, 5, 7, 15, 21, 35, and 105.
The 105 prime factors are 3, 5, and 7.

What’s the highest common factor between 97 and 105?
Factors of 97: 1, and 97.
The 105 factors are: 1, 3, 5, 7, 15, 21, 35, and 105.
GCF between 97 and 105: 1

What’s the highest common factor between 45 and 105?
Factors of 45: 1, 3, 5, 9, 15, and 45.
The 105 factors are: 1, 3, 5, 7, 15, 21, 35, and 105.
Common factors between 45 and 105 are 1, 3, 5, and 15.
GCF between 45 and 105: 15

Is 21 a factor of 105?
Yes, 21 is a factor of 105.
As 105 ÷ 5 = 21.

Is 10 a factor of 105?
No, 10 is not a factor of 105.
Because 105 ÷ 10 = leaves 5 as a remainder

## FAQs on Factors of 105

The FAQs on factors of 105 are given below:

List all the factors of 105
1, 3, 5, 7, 15, 21, 35, and 105 are the factors of 105.

What are the composite factors of 105?
15, 21, 35, and 105 are the composite factors of 105.

What are the factors of 105 in pairs?
(1, 105), (3, 35), (5, 21), and (7, 15) are the 105 factors in pairs.

What are the positive factors for 105?
1, 3, 5, 7, 15, 21, 35, and 105 are the positive factors for 105.

That is all for factors of 105. We hope this was easy to understand and has been useful for you. Although we hope there aren’t any doubts, if you do still have some, just feel free to message us in the comment section below, and we will reply with answers and explanations. Thank you for reading it till the end.

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Prerit Jain

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