# Factors of 60 in pair

Factors of 60 in pair are (1, 60) , (2, 30) , (3, 20) , (4, 15) , (5, 12) and (6, 10)

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

 1.   Steps to find factors of 60 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 60 in pair

Factor Pair Pair Factorization
1 and 60 1 x 60 = 60
2 and 30 2 x 30 = 60
3 and 20 3 x 20 = 60
4 and 15 4 x 15 = 60
5 and 12 5 x 12 = 60
6 and 10 6 x 10 = 60

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 60. They are called negative pair factors.

Hence, the negative pairs of 60 would be ( -1 , -60 ) .

#### 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 60 are 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60. So, factors of 60 in pair are (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

#### 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. 60 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 60.
• Every number is a factor of zero (0), since 60 x 0 = 0.
• 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, 4, 5, 6, 10, 12, 15, 20, 30, 60 are exact divisors of 60.
• Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Each factor divides 60 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 are all less than or equal to 60.

#### Steps to find Factors of 60

• Step 1. Find all the numbers that would divide 60 without leaving any remainder. Starting with the number 1 upto 30 (half of 60). The number 1 and the number itself are always factors of the given number.
60 ÷ 1 : Remainder = 0
60 ÷ 2 : Remainder = 0
60 ÷ 3 : Remainder = 0
60 ÷ 4 : Remainder = 0
60 ÷ 5 : Remainder = 0
60 ÷ 6 : Remainder = 0
60 ÷ 10 : Remainder = 0
60 ÷ 12 : Remainder = 0
60 ÷ 15 : Remainder = 0
60 ÷ 20 : Remainder = 0
60 ÷ 30 : Remainder = 0
60 ÷ 60 : Remainder = 0

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

• Is 60 a composite number?

Yes 60 is a composite number.

• Is 60 a prime number?

No 60 is not a prime number.

• What is the mean of factors of 60?

Factors of 60 are 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60. therefore mean of factors of 60 is (1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 + 60) / 12 = 14.00.

• 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

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 60.
- Writing all prime factors of 60.
- Writing all the possible factors of 60 in pair.
Help him in writing all these.

Positive factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Prime factors of 60 are 2, 2, 3, 5.
Factors of 60 in pair are (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

What are the pair factors of 60?

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Hence, the factors of 60 in pair are (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

Can you help Sammy list the factors of 60 and also find the factor pairs?

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Factors of 60 in pair are (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

The area of a rectangle is 60 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 60 in pair. So, the possible combinations (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

Help Diji in finding factors of 60 by Prime Factorization method and then sorting factors of 60 in pairs.

Prime factorization of 60 is 2 x 2 x 3 x 5. Factors of 60 in pair can be written as (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

Write the smallest prime factor of 60.

Smallest prime factor of 60 is 2.

Write the largest prime factor of 60.

Largest prime factor of 60 is 5.

Diji wants to write all the negative factors of 60. Can you help Diji in doing the same?

Negative factors of 60 are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30, -60.