# Factors of 105

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105

#### How to find factors of a number

 1.   Find factors of 105 using Division Method 2.   Find factors of 105 using Prime Factorization 3.   Find factors of 105 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 105

• Divide 105 by 1: 105 ÷ 1 : Remainder = 0
• Divide 105 by 3: 105 ÷ 3 : Remainder = 0
• Divide 105 by 5: 105 ÷ 5 : Remainder = 0
• Divide 105 by 7: 105 ÷ 7 : Remainder = 0
• Divide 105 by 15: 105 ÷ 15 : Remainder = 0
• Divide 105 by 21: 105 ÷ 21 : Remainder = 0
• Divide 105 by 35: 105 ÷ 35 : Remainder = 0
• Divide 105 by 105: 105 ÷ 105 : Remainder = 0

Hence, Factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105

#### 2. Steps to find factors of 105 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 105 using the division method, follow these steps:

• Step 1. Start dividing 105 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 105, which is 3. Divide 105 by 3 to obtain the quotient (35).
105 ÷ 3 = 35
• Step 3. Repeat step 1 with the obtained quotient (35).
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 105 is, 105 = 3 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 105 as shown below:

So, the prime factorization of 105 is, 105 = 3 x 5 x 7.

#### 3. Find factors of 105 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 105 would be the two numbers which, when multiplied, give 105 as the result.

The following table represents the calculation of factors of 105 in pairs:

Factor Pair Pair Factorization
1 and 105 1 x 105 = 105
3 and 35 3 x 35 = 105
5 and 21 5 x 21 = 105
7 and 15 7 x 15 = 105

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 105. They are called negative pair factors.

Hence, the negative pairs of 105 would be ( -1 , -105 ) , ( -3 , -35 ) , ( -5 , -21 ) and ( -7 , -15 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 15, 21, 35, 105 are exact divisors of 105.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 105 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 105.

• How do you find factors of a negative number? ( eg. -105 )?

Factors of -105 are -1, -3, -5, -7, -15, -21, -35, -105.

• What is the sum of all factors of 105?

The sum of all factors of 105 is 192.

• What is prime factorization of 105?

Prime factorization of 105 is 3 x 5 x 7.

• What are the pair factors of 105?

Pair factors of 105 are (1,105), (3,35), (5,21), (7,15).

• What are six multiples of 105?

First five multiples of 105 are 210, 315, 420, 525, 630, 735.

• Is 105 a whole number?

Yes 105 is a whole number.

• Which is the smallest prime factor of 105?

Smallest prime factor of 105 is 3.

• What are five multiples of 105?

First five multiples of 105 are 210, 315, 420, 525, 630.

• Write all factors of 105?

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.

#### Examples of Factors

Joey wants to write all the prime factors of 105 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 105 are 3, 5, 7.
So in exponential form it can be written as 3 x 5 x 7.

How many factors are there for 105?

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 105. Can you predict the answer?

7 factor(s) of 105 are 1, 3, 5, 7, 15, 21, 35.

Sammy is puzzled while calculating the prime factors of 105. Can you help him find them?

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.
Prime factors of 105 are 3, 5, 7

What is prime factorization of 105?

Prime factorization of 105 is 3 x 5 x 7 = 3 x 5 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 105. Can you help her?

Prime factors of 105 are 3, 5, 7.
Hence, the product of prime factors of 105.

Can you help Rubel to find out the product of the even factors of 105?

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.
Even factors of 105 are 0.
Hence, product of even factors of 105 is; 0 = 0.