Factors of 5400 in pair are (1, 5400) , (2, 2700) , (3, 1800) , (4, 1350) , (5, 1080) , (6, 900) , (8, 675) , (9, 600) , (10, 540) , (12, 450) , (15, 360) , (18, 300) , (20, 270) , (24, 225) , (25, 216) , (27, 200) , (30, 180) , (36, 150) , (40, 135) , (45, 120) , (50, 108) , (54, 100) , (60, 90) and (72, 75)

- Find all the numbers that would divide 5400 without leaving any remainder. Starting with the number 1 upto 2700 (half of 5400). The number 1 and the number itself are always factors of the given number.
- Pair the factors so that their product is 5400, and read off the answer!

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

1 and 5400 | 1 x 5400 = 5400 |

2 and 2700 | 2 x 2700 = 5400 |

3 and 1800 | 3 x 1800 = 5400 |

4 and 1350 | 4 x 1350 = 5400 |

5 and 1080 | 5 x 1080 = 5400 |

6 and 900 | 6 x 900 = 5400 |

8 and 675 | 8 x 675 = 5400 |

9 and 600 | 9 x 600 = 5400 |

10 and 540 | 10 x 540 = 5400 |

12 and 450 | 12 x 450 = 5400 |

15 and 360 | 15 x 360 = 5400 |

18 and 300 | 18 x 300 = 5400 |

20 and 270 | 20 x 270 = 5400 |

24 and 225 | 24 x 225 = 5400 |

25 and 216 | 25 x 216 = 5400 |

27 and 200 | 27 x 200 = 5400 |

30 and 180 | 30 x 180 = 5400 |

36 and 150 | 36 x 150 = 5400 |

40 and 135 | 40 x 135 = 5400 |

45 and 120 | 45 x 120 = 5400 |

50 and 108 | 50 x 108 = 5400 |

54 and 100 | 54 x 100 = 5400 |

60 and 90 | 60 x 90 = 5400 |

72 and 75 | 72 x 75 = 5400 |

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 5400. They are called negative pair factors.

Hence, the negative pairs of 5400 would be ( -1 , -5400 ) .

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 5400 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 12 , 15 , 18 , 20 , 24 , 25 , 27 , 30 , 36 , 40 , 45 , 50 , 54 , 60 , 72 , 75 , 90 , 100 , 108 , 120 , 135 , 150 , 180 , 200 , 216 , 225 , 270 , 300 , 360 , 450 , 540 , 600 , 675 , 900 , 1080 , 1350 , 1800 , 2700 , 5400. So, factors of 5400 in pair are (1,5400), (2,2700), (3,1800), (4,1350), (5,1080), (6,900), (8,675), (9,600), (10,540), (12,450), (15,360), (18,300), (20,270), (24,225), (25,216), (27,200), (30,180), (36,150), (40,135), (45,120), (50,108), (54,100), (60,90), (72,75).

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. 5400 is a factor of itself.
- 1 is a factor of every number. Eg. 1 is a factor of 5400.
- Every number is a factor of zero (0), since 5400 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, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400 are exact divisors of 5400.
- Factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400. Each factor divides 5400 without leaving a remainder.
- Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400 are all less than or equal to 5400.

**Step 1.**Find all the numbers that would divide 5400 without leaving any remainder. Starting with the number 1 upto 2700 (half of 5400). The number 1 and the number itself are always factors of the given number.5400 ÷ 1 : Remainder = 05400 ÷ 2 : Remainder = 05400 ÷ 3 : Remainder = 05400 ÷ 4 : Remainder = 05400 ÷ 5 : Remainder = 05400 ÷ 6 : Remainder = 05400 ÷ 8 : Remainder = 05400 ÷ 9 : Remainder = 05400 ÷ 10 : Remainder = 05400 ÷ 12 : Remainder = 05400 ÷ 15 : Remainder = 05400 ÷ 18 : Remainder = 05400 ÷ 20 : Remainder = 05400 ÷ 24 : Remainder = 05400 ÷ 25 : Remainder = 05400 ÷ 27 : Remainder = 05400 ÷ 30 : Remainder = 05400 ÷ 36 : Remainder = 05400 ÷ 40 : Remainder = 05400 ÷ 45 : Remainder = 05400 ÷ 50 : Remainder = 05400 ÷ 54 : Remainder = 05400 ÷ 60 : Remainder = 05400 ÷ 72 : Remainder = 05400 ÷ 75 : Remainder = 05400 ÷ 90 : Remainder = 05400 ÷ 100 : Remainder = 05400 ÷ 108 : Remainder = 05400 ÷ 120 : Remainder = 05400 ÷ 135 : Remainder = 05400 ÷ 150 : Remainder = 05400 ÷ 180 : Remainder = 05400 ÷ 200 : Remainder = 05400 ÷ 216 : Remainder = 05400 ÷ 225 : Remainder = 05400 ÷ 270 : Remainder = 05400 ÷ 300 : Remainder = 05400 ÷ 360 : Remainder = 05400 ÷ 450 : Remainder = 05400 ÷ 540 : Remainder = 05400 ÷ 600 : Remainder = 05400 ÷ 675 : Remainder = 05400 ÷ 900 : Remainder = 05400 ÷ 1080 : Remainder = 05400 ÷ 1350 : Remainder = 05400 ÷ 1800 : Remainder = 05400 ÷ 2700 : Remainder = 05400 ÷ 5400 : Remainder = 0

Hence, Factors of
*5400* are **1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, and 5400**

**Is 5400 a composite number?**Yes 5400 is a composite number.

**Is 5400 a prime number?**No 5400 is not a prime number.

**What is the mean of factors of 5400?**Factors of 5400 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 12 , 15 , 18 , 20 , 24 , 25 , 27 , 30 , 36 , 40 , 45 , 50 , 54 , 60 , 72 , 75 , 90 , 100 , 108 , 120 , 135 , 150 , 180 , 200 , 216 , 225 , 270 , 300 , 360 , 450 , 540 , 600 , 675 , 900 , 1080 , 1350 , 1800 , 2700 , 5400. therefore mean of factors of 5400 is (1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 25 + 27 + 30 + 36 + 40 + 45 + 50 + 54 + 60 + 72 + 75 + 90 + 100 + 108 + 120 + 135 + 150 + 180 + 200 + 216 + 225 + 270 + 300 + 360 + 450 + 540 + 600 + 675 + 900 + 1080 + 1350 + 1800 + 2700 + 5400) / 48 = 387.50.

**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.

Factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400. So, factors of 5400 in pair are (1,5400), (2,2700), (3,1800), (4,1350), (5,1080), (6,900), (8,675), (9,600), (10,540), (12,450), (15,360), (18,300), (20,270), (24,225), (25,216), (27,200), (30,180), (36,150), (40,135), (45,120), (50,108), (54,100), (60,90), (72,75).

Negative factors of 5400 are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -25, -27, -30, -36, -40, -45, -50, -54, -60, -72, -75, -90, -100, -108, -120, -135, -150, -180, -200, -216, -225, -270, -300, -360, -450, -540, -600, -675, -900, -1080, -1350, -1800, -2700, -5400. Hence, factors of 5400 in pair are (-1,-5400), (-2,-2700), (-3,-1800), (-4,-1350), (-5,-1080), (-6,-900), (-8,-675), (-9,-600), (-10,-540), (-12,-450), (-15,-360), (-18,-300), (-20,-270), (-24,-225), (-25,-216), (-27,-200), (-30,-180), (-36,-150), (-40,-135), (-45,-120), (-50,-108), (-54,-100), (-60,-90), (-72,-75).

Factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400. Positive factors of 5400 in pair are (1,5400), (2,2700), (3,1800), (4,1350), (5,1080), (6,900), (8,675), (9,600), (10,540), (12,450), (15,360), (18,300), (20,270), (24,225), (25,216), (27,200), (30,180), (36,150), (40,135), (45,120), (50,108), (54,100), (60,90), (72,75). Negative factors of 5400 in pair are (-1,-5400), (-2,-2700), (-3,-1800), (-4,-1350), (-5,-1080), (-6,-900), (-8,-675), (-9,-600), (-10,-540), (-12,-450), (-15,-360), (-18,-300), (-20,-270), (-24,-225), (-25,-216), (-27,-200), (-30,-180), (-36,-150), (-40,-135), (-45,-120), (-50,-108), (-54,-100), (-60,-90), (-72,-75).

Factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400. So the product of all factors of 5400 would be 1 x 2 x 3 x 4 x 5 x 6 x 8 x 9 x 10 x 12 x 15 x 18 x 20 x 24 x 25 x 27 x 30 x 36 x 40 x 45 x 50 x 54 x 60 x 72 x 75 x 90 x 100 x 108 x 120 x 135 x 150 x 180 x 200 x 216 x 225 x 270 x 300 x 360 x 450 x 540 x 600 x 675 x 900 x 1080 x 1350 x 1800 x 2700 x 5400 = 3.7796382529974633e+89.

Factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400. Prime factors are 2, 2, 2, 3, 3, 3, 5, 5. So, the product of all prime factors of 5400 would be 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 = 5400.

Factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400.

Factors of 5400 in pair are (1,5400), (2,2700), (3,1800), (4,1350), (5,1080), (6,900), (8,675), (9,600), (10,540), (12,450), (15,360), (18,300), (20,270), (24,225), (25,216), (27,200), (30,180), (36,150), (40,135), (45,120), (50,108), (54,100), (60,90), (72,75).

To arrange 5400 blocks in all possible ways to form a rectangle, we need to calculate factors of 5400 in pair. Therefore, factors of 5400 in pair are (1,5400), (2,2700), (3,1800), (4,1350), (5,1080), (6,900), (8,675), (9,600), (10,540), (12,450), (15,360), (18,300), (20,270), (24,225), (25,216), (27,200), (30,180), (36,150), (40,135), (45,120), (50,108), (54,100), (60,90), (72,75)