Factors of 900 in pair are (1, 900) , (2, 450) , (3, 300) , (4, 225) , (5, 180) , (6, 150) , (9, 100) , (10, 90) , (12, 75) , (15, 60) , (18, 50) , (20, 45) , (25, 36) and (30, 30)

How to find factors of a number in pair

Steps to find factors of 900 in pair

Example: Find factors of 900 in pair

Factor Pair Pair Factorization
1 and 900 1 x 900 = 900
2 and 450 2 x 450 = 900
3 and 300 3 x 300 = 900
4 and 225 4 x 225 = 900
5 and 180 5 x 180 = 900
6 and 150 6 x 150 = 900
9 and 100 9 x 100 = 900
10 and 90 10 x 90 = 900
12 and 75 12 x 75 = 900
15 and 60 15 x 60 = 900
18 and 50 18 x 50 = 900
20 and 45 20 x 45 = 900
25 and 36 25 x 36 = 900
30 and 30 30 x 30 = 900

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 900. They are called negative pair factors.

Hence, the negative pairs of 900 would be ( -1 , -900 ) .

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 900 are 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 12 , 15 , 18 , 20 , 25 , 30 , 36 , 45 , 50 , 60 , 75 , 90 , 100 , 150 , 180 , 225 , 300 , 450 , 900. So, factors of 900 in pair are (1,900), (2,450), (3,300), (4,225), (5,180), (6,150), (9,100), (10,90), (12,75), (15,60), (18,50), (20,45), (25,36), (30,30).

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. 900 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 900.
  • Every number is a factor of zero (0), since 900 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, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900 are exact divisors of 900.
  • Factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900. Each factor divides 900 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, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900 are all less than or equal to 900.

Steps to find Factors of 900

  • Step 1. Find all the numbers that would divide 900 without leaving any remainder. Starting with the number 1 upto 450 (half of 900). The number 1 and the number itself are always factors of the given number.
    900 ÷ 1 : Remainder = 0
    900 ÷ 2 : Remainder = 0
    900 ÷ 3 : Remainder = 0
    900 ÷ 4 : Remainder = 0
    900 ÷ 5 : Remainder = 0
    900 ÷ 6 : Remainder = 0
    900 ÷ 9 : Remainder = 0
    900 ÷ 10 : Remainder = 0
    900 ÷ 12 : Remainder = 0
    900 ÷ 15 : Remainder = 0
    900 ÷ 18 : Remainder = 0
    900 ÷ 20 : Remainder = 0
    900 ÷ 25 : Remainder = 0
    900 ÷ 30 : Remainder = 0
    900 ÷ 36 : Remainder = 0
    900 ÷ 45 : Remainder = 0
    900 ÷ 50 : Remainder = 0
    900 ÷ 60 : Remainder = 0
    900 ÷ 75 : Remainder = 0
    900 ÷ 90 : Remainder = 0
    900 ÷ 100 : Remainder = 0
    900 ÷ 150 : Remainder = 0
    900 ÷ 180 : Remainder = 0
    900 ÷ 225 : Remainder = 0
    900 ÷ 300 : Remainder = 0
    900 ÷ 450 : Remainder = 0
    900 ÷ 900 : Remainder = 0

Hence, Factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900

Frequently Asked Questions

  • Is 900 a composite number?

    Yes 900 is a composite number.

  • Is 900 a prime number?

    No 900 is not a prime number.

  • What is the mean of factors of 900?

    Factors of 900 are 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 12 , 15 , 18 , 20 , 25 , 30 , 36 , 45 , 50 , 60 , 75 , 90 , 100 , 150 , 180 , 225 , 300 , 450 , 900. therefore mean of factors of 900 is (1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 300 + 450 + 900) / 27 = 104.48.

  • 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 900.
- Writing all prime factors of 900.
- Writing all the possible factors of 900 in pair.
Help him in writing all these.

Positive factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900.
Prime factors of 900 are 2, 2, 3, 3, 5, 5.
Factors of 900 in pair are (1,900), (2,450), (3,300), (4,225), (5,180), (6,150), (9,100), (10,90), (12,75), (15,60), (18,50), (20,45), (25,36), (30,30).

What are the pair factors of 900?

Factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900. Hence, the factors of 900 in pair are (1,900), (2,450), (3,300), (4,225), (5,180), (6,150), (9,100), (10,90), (12,75), (15,60), (18,50), (20,45), (25,36), (30,30).

Can you help Sammy list the factors of 900 and also find the factor pairs?

Factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900.
Factors of 900 in pair are (1,900), (2,450), (3,300), (4,225), (5,180), (6,150), (9,100), (10,90), (12,75), (15,60), (18,50), (20,45), (25,36), (30,30).

The area of a rectangle is 900 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 900 in pair. So, the possible combinations (1,900), (2,450), (3,300), (4,225), (5,180), (6,150), (9,100), (10,90), (12,75), (15,60), (18,50), (20,45), (25,36), (30,30).

Help Diji in finding factors of 900 by Prime Factorization method and then sorting factors of 900 in pairs.

Prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5. Factors of 900 in pair can be written as (1,900), (2,450), (3,300), (4,225), (5,180), (6,150), (9,100), (10,90), (12,75), (15,60), (18,50), (20,45), (25,36), (30,30).

Write the smallest prime factor of 900.

Smallest prime factor of 900 is 2.

Write the largest prime factor of 900.

Largest prime factor of 900 is 5.

Diji wants to write all the negative factors of 900. Can you help Diji in doing the same?

Negative factors of 900 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -150, -180, -225, -300, -450, -900.