Factors of 180 in pair are (1, 180) , (2, 90) , (3, 60) , (4, 45) , (5, 36) , (6, 30) , (9, 20) , (10, 18) and (12, 15)

How to find factors of a number in pair

Steps to find factors of 180 in pair

Example: Find factors of 180 in pair

Factor Pair Pair Factorization
1 and 180 1 x 180 = 180
2 and 90 2 x 90 = 180
3 and 60 3 x 60 = 180
4 and 45 4 x 45 = 180
5 and 36 5 x 36 = 180
6 and 30 6 x 30 = 180
9 and 20 9 x 20 = 180
10 and 18 10 x 18 = 180
12 and 15 12 x 15 = 180

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 180. They are called negative pair factors.

Hence, the negative pairs of 180 would be ( -1 , -180 ) .

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 180 are 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 12 , 15 , 18 , 20 , 30 , 36 , 45 , 60 , 90 , 180. So, factors of 180 in pair are (1,180), (2,90), (3,60), (4,45), (5,36), (6,30), (9,20), (10,18), (12,15).

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

  • Each number is a factor of itself. Eg. 180 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 180.
  • Every number is a factor of zero (0), since 180 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, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are exact divisors of 180.
  • Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. Each factor divides 180 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are all less than or equal to 180.

Steps to find Factors of 180

  • Step 1. Find all the numbers that would divide 180 without leaving any remainder. Starting with the number 1 upto 90 (half of 180). The number 1 and the number itself are always factors of the given number.
    180 ÷ 1 : Remainder = 0
    180 ÷ 2 : Remainder = 0
    180 ÷ 3 : Remainder = 0
    180 ÷ 4 : Remainder = 0
    180 ÷ 5 : Remainder = 0
    180 ÷ 6 : Remainder = 0
    180 ÷ 9 : Remainder = 0
    180 ÷ 10 : Remainder = 0
    180 ÷ 12 : Remainder = 0
    180 ÷ 15 : Remainder = 0
    180 ÷ 18 : Remainder = 0
    180 ÷ 20 : Remainder = 0
    180 ÷ 30 : Remainder = 0
    180 ÷ 36 : Remainder = 0
    180 ÷ 45 : Remainder = 0
    180 ÷ 60 : Remainder = 0
    180 ÷ 90 : Remainder = 0
    180 ÷ 180 : Remainder = 0

Hence, Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180

Frequently Asked Questions

  • Is 180 a composite number?

    Yes 180 is a composite number.

  • Is 180 a prime number?

    No 180 is not a prime number.

  • What is the mean of factors of 180?

    Factors of 180 are 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 12 , 15 , 18 , 20 , 30 , 36 , 45 , 60 , 90 , 180. therefore mean of factors of 180 is (1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 + 180) / 18 = 30.33.

  • 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 180.
- Writing all prime factors of 180.
- Writing all the possible factors of 180 in pair.
Help him in writing all these.

Positive factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Prime factors of 180 are 2, 2, 3, 3, 5.
Factors of 180 in pair are (1,180), (2,90), (3,60), (4,45), (5,36), (6,30), (9,20), (10,18), (12,15).

What are the pair factors of 180?

Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. Hence, the factors of 180 in pair are (1,180), (2,90), (3,60), (4,45), (5,36), (6,30), (9,20), (10,18), (12,15).

Can you help Sammy list the factors of 180 and also find the factor pairs?

Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Factors of 180 in pair are (1,180), (2,90), (3,60), (4,45), (5,36), (6,30), (9,20), (10,18), (12,15).

The area of a rectangle is 180 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 180 in pair. So, the possible combinations (1,180), (2,90), (3,60), (4,45), (5,36), (6,30), (9,20), (10,18), (12,15).

Help Diji in finding factors of 180 by Prime Factorization method and then sorting factors of 180 in pairs.

Prime factorization of 180 is 2 x 2 x 3 x 3 x 5. Factors of 180 in pair can be written as (1,180), (2,90), (3,60), (4,45), (5,36), (6,30), (9,20), (10,18), (12,15).

Write the smallest prime factor of 180.

Smallest prime factor of 180 is 2.

Write the largest prime factor of 180.

Largest prime factor of 180 is 5.

Diji wants to write all the negative factors of 180. Can you help Diji in doing the same?

Negative factors of 180 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, -180.