# Factors of 105 in pair

Factors of 105 in pair are (1, 105) , (3, 35) , (5, 21) and (7, 15)

#### How to find factors of a number in pair

 1.   Steps to find factors of 105 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 105 in pair

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 ) .

#### Definition of factor pairs?

In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 105 are 1 , 3 , 5 , 7 , 15 , 21 , 35 , 105. So, factors of 105 in pair are (1,105), (3,35), (5,21), (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.

#### Steps to find Factors of 105

• Step 1. Find all the numbers that would divide 105 without leaving any remainder. Starting with the number 1 upto 52 (half of 105). The number 1 and the number itself are always factors of the given number.
105 ÷ 1 : Remainder = 0
105 ÷ 3 : Remainder = 0
105 ÷ 5 : Remainder = 0
105 ÷ 7 : Remainder = 0
105 ÷ 15 : Remainder = 0
105 ÷ 21 : Remainder = 0
105 ÷ 35 : Remainder = 0
105 ÷ 105 : Remainder = 0

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

• Is 105 a composite number?

Yes 105 is a composite number.

• Is 105 a perfect square?

No 105 is not a perfect square.

• Write all odd factors of 105?

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.
Odd factors of 105 are 1 , 3 , 5 , 7 , 15 , 21 , 35 , 105.

• What is the mean of all prime factors of 105?

Factors of 105 are 1 , 3 , 5 , 7 , 15 , 21 , 35 , 105. Prime factors of 105 are 3 , 5 , 7. Therefore mean of prime factors of 105 is (3 + 5 + 7) / 3 = 5.00.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

#### Examples of Factors

Can you help Rubel in arranging 105 blocks in order to form a rectangle in all possible ways? For arranging 105 blocks in order to form a rectangle in all possible ways we need to find factors of 105 in pair.

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. So, factors of 105 in pair are (1,105), (3,35), (5,21), (7,15).

How many total number of factors of 105 in pair are possible?

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. Hence, the factors of 105 in pair are (1,105), (3,35), (5,21), (7,15). Therefore, in total 4 pairs of factors are possible.

Sammy wants to write all the negative factors of 105 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 105 are -1, -3, -5, -7, -15, -21, -35, -105. Hence, factors of 105 in pair are (-1,-105), (-3,-35), (-5,-21), (-7,-15).

Find the product of all prime factors of 105.

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. Prime factors are 3, 5, 7. So, the product of all prime factors of 105 would be 3 x 5 x 7 = 105.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 105.
- Writing all prime factors of 105.
- Writing all the possible factors of 105 in pair.
Help him in writing all these.

Positive factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.
Prime factors of 105 are 3, 5, 7.
Factors of 105 in pair are (1,105), (3,35), (5,21), (7,15).

Can you help Sammy list the factors of 105 and also find the factor pairs?

Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.
Factors of 105 in pair are (1,105), (3,35), (5,21), (7,15).

Help Diji in finding factors of 105 by Prime Factorization method and then sorting factors of 105 in pairs.

Prime factorization of 105 is 3 x 5 x 7. Factors of 105 in pair can be written as (1,105), (3,35), (5,21), (7,15).

Write the smallest prime factor of 105.

Smallest prime factor of 105 is 3.