# Factors of 30 in pair

Factors of 30 in pair are (1, 30) , (2, 15) , (3, 10) and (5, 6)

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

 1.   Steps to find factors of 30 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 30 in pair

Factor Pair Pair Factorization
1 and 30 1 x 30 = 30
2 and 15 2 x 15 = 30
3 and 10 3 x 10 = 30
5 and 6 5 x 6 = 30

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 30. They are called negative pair factors.

Hence, the negative pairs of 30 would be ( -1 , -30 ) .

#### 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 30 are 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30. So, factors of 30 in pair are (1,30), (2,15), (3,10), (5,6).

#### 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

• Each number is a factor of itself. Eg. 30 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 10, 15, 30 are exact divisors of 30.
• 1 is a factor of every number. Eg. 1 is a factor of 30.
• Every number is a factor of zero (0), since 30 x 0 = 0.

#### Steps to find Factors of 30

• Step 1. Find all the numbers that would divide 30 without leaving any remainder. Starting with the number 1 upto 15 (half of 30). The number 1 and the number itself are always factors of the given number.
30 ÷ 1 : Remainder = 0
30 ÷ 2 : Remainder = 0
30 ÷ 3 : Remainder = 0
30 ÷ 5 : Remainder = 0
30 ÷ 6 : Remainder = 0
30 ÷ 10 : Remainder = 0
30 ÷ 15 : Remainder = 0
30 ÷ 30 : Remainder = 0

Hence, Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30

• Is 30 a composite number?

Yes 30 is a composite number.

• Is 30 a prime number?

No 30 is not a prime number.

• What is the mean of factors of 30?

Factors of 30 are 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30. therefore mean of factors of 30 is (1 + 2 + 3 + 5 + 6 + 10 + 15 + 30) / 8 = 9.00.

• 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.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Can you help Rubel in arranging 30 blocks in order to form a rectangle in all possible ways? For arranging 30 blocks in order to form a rectangle in all possible ways we need to find factors of 30 in pair.

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. So, factors of 30 in pair are (1,30), (2,15), (3,10), (5,6).

Ariel has been asked to write all factor pairs of 30 but she is finding it difficult. Can you help her find out?

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. So, factors of 30 in pair are (1,30), (2,15), (3,10), (5,6).

How many total number of factors of 30 in pair are possible?

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. Hence, the factors of 30 in pair are (1,30), (2,15), (3,10), (5,6). Therefore, in total 4 pairs of factors are possible.

Sammy wants to write all the negative factors of 30 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 30 are -1, -2, -3, -5, -6, -10, -15, -30. Hence, factors of 30 in pair are (-1,-30), (-2,-15), (-3,-10), (-5,-6).

Help Deep in writing the positive factors of 30 in pair and negative factor of 30 in pair.

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. Positive factors of 30 in pair are (1,30), (2,15), (3,10), (5,6). Negative factors of 30 in pair are (-1,-30), (-2,-15), (-3,-10), (-5,-6).

Find the product of all factors of 30.

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. So the product of all factors of 30 would be 1 x 2 x 3 x 5 x 6 x 10 x 15 x 30 = 810000.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 30.
- Writing all prime factors of 30.
- Writing all the possible factors of 30 in pair.
Help him in writing all these.

Positive factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
Prime factors of 30 are 2, 3, 5.
Factors of 30 in pair are (1,30), (2,15), (3,10), (5,6).

Can you help Sammy list the factors of 30 and also find the factor pairs?

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 30 in pair are (1,30), (2,15), (3,10), (5,6).