Factors of 2700 in pair are (1, 2700) , (2, 1350) , (3, 900) , (4, 675) , (5, 540) , (6, 450) , (9, 300) , (10, 270) , (12, 225) , (15, 180) , (18, 150) , (20, 135) , (25, 108) , (27, 100) , (30, 90) , (36, 75) , (45, 60) and (50, 54)

- Find all the numbers that would divide 2700 without leaving any remainder. Starting with the number 1 upto 1350 (half of 2700). The number 1 and the number itself are always factors of the given number.
- Pair the factors so that their product is 2700, and read off the answer!

Factor Pair | Pair Factorization |
---|---|

1 and 2700 | 1 x 2700 = 2700 |

2 and 1350 | 2 x 1350 = 2700 |

3 and 900 | 3 x 900 = 2700 |

4 and 675 | 4 x 675 = 2700 |

5 and 540 | 5 x 540 = 2700 |

6 and 450 | 6 x 450 = 2700 |

9 and 300 | 9 x 300 = 2700 |

10 and 270 | 10 x 270 = 2700 |

12 and 225 | 12 x 225 = 2700 |

15 and 180 | 15 x 180 = 2700 |

18 and 150 | 18 x 150 = 2700 |

20 and 135 | 20 x 135 = 2700 |

25 and 108 | 25 x 108 = 2700 |

27 and 100 | 27 x 100 = 2700 |

30 and 90 | 30 x 90 = 2700 |

36 and 75 | 36 x 75 = 2700 |

45 and 60 | 45 x 60 = 2700 |

50 and 54 | 50 x 54 = 2700 |

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 2700. They are called negative pair factors.

Hence, the negative pairs of 2700 would be ( -1 , -2700 ) .

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 2700 are 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 12 , 15 , 18 , 20 , 25 , 27 , 30 , 36 , 45 , 50 , 54 , 60 , 75 , 90 , 100 , 108 , 135 , 150 , 180 , 225 , 270 , 300 , 450 , 540 , 675 , 900 , 1350 , 2700. So, factors of 2700 in pair are (1,2700), (2,1350), (3,900), (4,675), (5,540), (6,450), (9,300), (10,270), (12,225), (15,180), (18,150), (20,135), (25,108), (27,100), (30,90), (36,75), (45,60), (50,54).

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.

- Each number is a factor of itself. Eg. 2700 is a factor of itself.
- 1 is a factor of every number. Eg. 1 is a factor of 2700.
- Every number is a factor of zero (0), since 2700 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, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700 are exact divisors of 2700.
- Factors of 2700 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700. Each factor divides 2700 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, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700 are all less than or equal to 2700.

**Step 1.**Find all the numbers that would divide 2700 without leaving any remainder. Starting with the number 1 upto 1350 (half of 2700). The number 1 and the number itself are always factors of the given number.2700 ÷ 1 : Remainder = 02700 ÷ 2 : Remainder = 02700 ÷ 3 : Remainder = 02700 ÷ 4 : Remainder = 02700 ÷ 5 : Remainder = 02700 ÷ 6 : Remainder = 02700 ÷ 9 : Remainder = 02700 ÷ 10 : Remainder = 02700 ÷ 12 : Remainder = 02700 ÷ 15 : Remainder = 02700 ÷ 18 : Remainder = 02700 ÷ 20 : Remainder = 02700 ÷ 25 : Remainder = 02700 ÷ 27 : Remainder = 02700 ÷ 30 : Remainder = 02700 ÷ 36 : Remainder = 02700 ÷ 45 : Remainder = 02700 ÷ 50 : Remainder = 02700 ÷ 54 : Remainder = 02700 ÷ 60 : Remainder = 02700 ÷ 75 : Remainder = 02700 ÷ 90 : Remainder = 02700 ÷ 100 : Remainder = 02700 ÷ 108 : Remainder = 02700 ÷ 135 : Remainder = 02700 ÷ 150 : Remainder = 02700 ÷ 180 : Remainder = 02700 ÷ 225 : Remainder = 02700 ÷ 270 : Remainder = 02700 ÷ 300 : Remainder = 02700 ÷ 450 : Remainder = 02700 ÷ 540 : Remainder = 02700 ÷ 675 : Remainder = 02700 ÷ 900 : Remainder = 02700 ÷ 1350 : Remainder = 02700 ÷ 2700 : Remainder = 0

Hence, Factors of
*2700* are **1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, and 2700**

**Is 2700 a composite number?**Yes 2700 is a composite number.

**Is 2700 a prime number?**No 2700 is not a prime number.

**What is the mean of factors of 2700?**Factors of 2700 are 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 12 , 15 , 18 , 20 , 25 , 27 , 30 , 36 , 45 , 50 , 54 , 60 , 75 , 90 , 100 , 108 , 135 , 150 , 180 , 225 , 270 , 300 , 450 , 540 , 675 , 900 , 1350 , 2700. therefore mean of factors of 2700 is (1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 27 + 30 + 36 + 45 + 50 + 54 + 60 + 75 + 90 + 100 + 108 + 135 + 150 + 180 + 225 + 270 + 300 + 450 + 540 + 675 + 900 + 1350 + 2700) / 36 = 241.11.

**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.

- Finding out all positive factors of 2700.

- Writing all prime factors of 2700.

- Writing all the possible factors of 2700 in pair.

Help him in writing all these.

Positive factors of 2700 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700.

Prime factors of 2700 are 2, 2, 3, 3, 3, 5, 5.

Factors of 2700 in pair are (1,2700), (2,1350), (3,900), (4,675), (5,540), (6,450), (9,300), (10,270), (12,225), (15,180), (18,150), (20,135), (25,108), (27,100), (30,90), (36,75), (45,60), (50,54).

Factors of 2700 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700. Hence, the factors of 2700 in pair are (1,2700), (2,1350), (3,900), (4,675), (5,540), (6,450), (9,300), (10,270), (12,225), (15,180), (18,150), (20,135), (25,108), (27,100), (30,90), (36,75), (45,60), (50,54).

Factors of 2700 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700.

Factors of 2700 in pair are (1,2700), (2,1350), (3,900), (4,675), (5,540), (6,450), (9,300), (10,270), (12,225), (15,180), (18,150), (20,135), (25,108), (27,100), (30,90), (36,75), (45,60), (50,54).

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 2700 in pair. So, the possible combinations (1,2700), (2,1350), (3,900), (4,675), (5,540), (6,450), (9,300), (10,270), (12,225), (15,180), (18,150), (20,135), (25,108), (27,100), (30,90), (36,75), (45,60), (50,54).

Prime factorization of 2700 is 2 x 2 x 3 x 3 x 3 x 5 x 5. Factors of 2700 in pair can be written as (1,2700), (2,1350), (3,900), (4,675), (5,540), (6,450), (9,300), (10,270), (12,225), (15,180), (18,150), (20,135), (25,108), (27,100), (30,90), (36,75), (45,60), (50,54).

Smallest prime factor of 2700 is 2.

Largest prime factor of 2700 is 5.

Negative factors of 2700 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -27, -30, -36, -45, -50, -54, -60, -75, -90, -100, -108, -135, -150, -180, -225, -270, -300, -450, -540, -675, -900, -1350, -2700.