Factors of 2100 in pair are (1, 2100) , (2, 1050) , (3, 700) , (4, 525) , (5, 420) , (6, 350) , (7, 300) , (10, 210) , (12, 175) , (14, 150) , (15, 140) , (20, 105) , (21, 100) , (25, 84) , (28, 75) , (30, 70) , (35, 60) and (42, 50)

How to find factors of a number in pair

Steps to find factors of 2100 in pair

Example: Find factors of 2100 in pair

Factor Pair Pair Factorization
1 and 2100 1 x 2100 = 2100
2 and 1050 2 x 1050 = 2100
3 and 700 3 x 700 = 2100
4 and 525 4 x 525 = 2100
5 and 420 5 x 420 = 2100
6 and 350 6 x 350 = 2100
7 and 300 7 x 300 = 2100
10 and 210 10 x 210 = 2100
12 and 175 12 x 175 = 2100
14 and 150 14 x 150 = 2100
15 and 140 15 x 140 = 2100
20 and 105 20 x 105 = 2100
21 and 100 21 x 100 = 2100
25 and 84 25 x 84 = 2100
28 and 75 28 x 75 = 2100
30 and 70 30 x 70 = 2100
35 and 60 35 x 60 = 2100
42 and 50 42 x 50 = 2100

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 2100. They are called negative pair factors.

Hence, the negative pairs of 2100 would be ( -1 , -2100 ) .

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 2100 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 21 , 25 , 28 , 30 , 35 , 42 , 50 , 60 , 70 , 75 , 84 , 100 , 105 , 140 , 150 , 175 , 210 , 300 , 350 , 420 , 525 , 700 , 1050 , 2100. So, factors of 2100 in pair are (1,2100), (2,1050), (3,700), (4,525), (5,420), (6,350), (7,300), (10,210), (12,175), (14,150), (15,140), (20,105), (21,100), (25,84), (28,75), (30,70), (35,60), (42,50).

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. 2100 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2100.
  • Every number is a factor of zero (0), since 2100 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, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100 are exact divisors of 2100.
  • Factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100. Each factor divides 2100 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100 are all less than or equal to 2100.

Steps to find Factors of 2100

  • Step 1. Find all the numbers that would divide 2100 without leaving any remainder. Starting with the number 1 upto 1050 (half of 2100). The number 1 and the number itself are always factors of the given number.
    2100 ÷ 1 : Remainder = 0
    2100 ÷ 2 : Remainder = 0
    2100 ÷ 3 : Remainder = 0
    2100 ÷ 4 : Remainder = 0
    2100 ÷ 5 : Remainder = 0
    2100 ÷ 6 : Remainder = 0
    2100 ÷ 7 : Remainder = 0
    2100 ÷ 10 : Remainder = 0
    2100 ÷ 12 : Remainder = 0
    2100 ÷ 14 : Remainder = 0
    2100 ÷ 15 : Remainder = 0
    2100 ÷ 20 : Remainder = 0
    2100 ÷ 21 : Remainder = 0
    2100 ÷ 25 : Remainder = 0
    2100 ÷ 28 : Remainder = 0
    2100 ÷ 30 : Remainder = 0
    2100 ÷ 35 : Remainder = 0
    2100 ÷ 42 : Remainder = 0
    2100 ÷ 50 : Remainder = 0
    2100 ÷ 60 : Remainder = 0
    2100 ÷ 70 : Remainder = 0
    2100 ÷ 75 : Remainder = 0
    2100 ÷ 84 : Remainder = 0
    2100 ÷ 100 : Remainder = 0
    2100 ÷ 105 : Remainder = 0
    2100 ÷ 140 : Remainder = 0
    2100 ÷ 150 : Remainder = 0
    2100 ÷ 175 : Remainder = 0
    2100 ÷ 210 : Remainder = 0
    2100 ÷ 300 : Remainder = 0
    2100 ÷ 350 : Remainder = 0
    2100 ÷ 420 : Remainder = 0
    2100 ÷ 525 : Remainder = 0
    2100 ÷ 700 : Remainder = 0
    2100 ÷ 1050 : Remainder = 0
    2100 ÷ 2100 : Remainder = 0

Hence, Factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, and 2100

Frequently Asked Questions

  • Is 2100 a composite number?

    Yes 2100 is a composite number.

  • Is 2100 a prime number?

    No 2100 is not a prime number.

  • What is the mean of factors of 2100?

    Factors of 2100 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 21 , 25 , 28 , 30 , 35 , 42 , 50 , 60 , 70 , 75 , 84 , 100 , 105 , 140 , 150 , 175 , 210 , 300 , 350 , 420 , 525 , 700 , 1050 , 2100. therefore mean of factors of 2100 is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 14 + 15 + 20 + 21 + 25 + 28 + 30 + 35 + 42 + 50 + 60 + 70 + 75 + 84 + 100 + 105 + 140 + 150 + 175 + 210 + 300 + 350 + 420 + 525 + 700 + 1050 + 2100) / 36 = 192.89.

  • 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 2100.
- Writing all prime factors of 2100.
- Writing all the possible factors of 2100 in pair.
Help him in writing all these.

Positive factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100.
Prime factors of 2100 are 2, 2, 3, 5, 5, 7.
Factors of 2100 in pair are (1,2100), (2,1050), (3,700), (4,525), (5,420), (6,350), (7,300), (10,210), (12,175), (14,150), (15,140), (20,105), (21,100), (25,84), (28,75), (30,70), (35,60), (42,50).

What are the pair factors of 2100?

Factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100. Hence, the factors of 2100 in pair are (1,2100), (2,1050), (3,700), (4,525), (5,420), (6,350), (7,300), (10,210), (12,175), (14,150), (15,140), (20,105), (21,100), (25,84), (28,75), (30,70), (35,60), (42,50).

Can you help Sammy list the factors of 2100 and also find the factor pairs?

Factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100.
Factors of 2100 in pair are (1,2100), (2,1050), (3,700), (4,525), (5,420), (6,350), (7,300), (10,210), (12,175), (14,150), (15,140), (20,105), (21,100), (25,84), (28,75), (30,70), (35,60), (42,50).

The area of a rectangle is 2100 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 2100 in pair. So, the possible combinations (1,2100), (2,1050), (3,700), (4,525), (5,420), (6,350), (7,300), (10,210), (12,175), (14,150), (15,140), (20,105), (21,100), (25,84), (28,75), (30,70), (35,60), (42,50).

Help Diji in finding factors of 2100 by Prime Factorization method and then sorting factors of 2100 in pairs.

Prime factorization of 2100 is 2 x 2 x 3 x 5 x 5 x 7. Factors of 2100 in pair can be written as (1,2100), (2,1050), (3,700), (4,525), (5,420), (6,350), (7,300), (10,210), (12,175), (14,150), (15,140), (20,105), (21,100), (25,84), (28,75), (30,70), (35,60), (42,50).

Write the smallest prime factor of 2100.

Smallest prime factor of 2100 is 2.

Write the largest prime factor of 2100.

Largest prime factor of 2100 is 7.

Diji wants to write all the negative factors of 2100. Can you help Diji in doing the same?

Negative factors of 2100 are -1, -2, -3, -4, -5, -6, -7, -10, -12, -14, -15, -20, -21, -25, -28, -30, -35, -42, -50, -60, -70, -75, -84, -100, -105, -140, -150, -175, -210, -300, -350, -420, -525, -700, -1050, -2100.