Factors of 1872 in pair are (1, 1872) , (2, 936) , (3, 624) , (4, 468) , (6, 312) , (8, 234) , (9, 208) , (12, 156) , (13, 144) , (16, 117) , (18, 104) , (24, 78) , (26, 72) , (36, 52) and (39, 48)

- Find all the numbers that would divide 1872 without leaving any remainder. Starting with the number 1 upto 936 (half of 1872). The number 1 and the number itself are always factors of the given number.
- Pair the factors so that their product is 1872, and read off the answer!

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

1 and 1872 | 1 x 1872 = 1872 |

2 and 936 | 2 x 936 = 1872 |

3 and 624 | 3 x 624 = 1872 |

4 and 468 | 4 x 468 = 1872 |

6 and 312 | 6 x 312 = 1872 |

8 and 234 | 8 x 234 = 1872 |

9 and 208 | 9 x 208 = 1872 |

12 and 156 | 12 x 156 = 1872 |

13 and 144 | 13 x 144 = 1872 |

16 and 117 | 16 x 117 = 1872 |

18 and 104 | 18 x 104 = 1872 |

24 and 78 | 24 x 78 = 1872 |

26 and 72 | 26 x 72 = 1872 |

36 and 52 | 36 x 52 = 1872 |

39 and 48 | 39 x 48 = 1872 |

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 1872. They are called negative pair factors.

Hence, the negative pairs of 1872 would be ( -1 , -1872 ) .

A factor pair of a number can be defined as the combination of two factors in such a way that when multiplied together produce the number itself. Every natural number is a product of atleast one factor pair. Eg- Factors of 1872 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 13 , 16 , 18 , 24 , 26 , 36 , 39 , 48 , 52 , 72 , 78 , 104 , 117 , 144 , 156 , 208 , 234 , 312 , 468 , 624 , 936 , 1872. So, factors of 1872 in pair are (1,1872), (2,936), (3,624), (4,468), (6,312), (8,234), (9,208), (12,156), (13,144), (16,117), (18,104), (24,78), (26,72), (36,52), (39,48).

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

- Each number is a factor of itself. Eg. 1872 is a factor of itself.
- 1 is a factor of every number. Eg. 1 is a factor of 1872.
- Every number is a factor of zero (0), since 1872 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, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872 are exact divisors of 1872.
- Factors of 1872 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872. Each factor divides 1872 without leaving a remainder.
- Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872 are all less than or equal to 1872.

**Step 1.**Find all the numbers that would divide 1872 without leaving any remainder. Starting with the number 1 upto 936 (half of 1872). The number 1 and the number itself are always factors of the given number.1872 ÷ 1 : Remainder = 01872 ÷ 2 : Remainder = 01872 ÷ 3 : Remainder = 01872 ÷ 4 : Remainder = 01872 ÷ 6 : Remainder = 01872 ÷ 8 : Remainder = 01872 ÷ 9 : Remainder = 01872 ÷ 12 : Remainder = 01872 ÷ 13 : Remainder = 01872 ÷ 16 : Remainder = 01872 ÷ 18 : Remainder = 01872 ÷ 24 : Remainder = 01872 ÷ 26 : Remainder = 01872 ÷ 36 : Remainder = 01872 ÷ 39 : Remainder = 01872 ÷ 48 : Remainder = 01872 ÷ 52 : Remainder = 01872 ÷ 72 : Remainder = 01872 ÷ 78 : Remainder = 01872 ÷ 104 : Remainder = 01872 ÷ 117 : Remainder = 01872 ÷ 144 : Remainder = 01872 ÷ 156 : Remainder = 01872 ÷ 208 : Remainder = 01872 ÷ 234 : Remainder = 01872 ÷ 312 : Remainder = 01872 ÷ 468 : Remainder = 01872 ÷ 624 : Remainder = 01872 ÷ 936 : Remainder = 01872 ÷ 1872 : Remainder = 0

Hence, Factors of
*1872* are **1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, and 1872**

**Is 1872 a composite number?**Yes 1872 is a composite number.

**Is 1872 a prime number?**No 1872 is not a prime number.

**What is the mean of factors of 1872?**Factors of 1872 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 13 , 16 , 18 , 24 , 26 , 36 , 39 , 48 , 52 , 72 , 78 , 104 , 117 , 144 , 156 , 208 , 234 , 312 , 468 , 624 , 936 , 1872. therefore mean of factors of 1872 is (1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 13 + 16 + 18 + 24 + 26 + 36 + 39 + 48 + 52 + 72 + 78 + 104 + 117 + 144 + 156 + 208 + 234 + 312 + 468 + 624 + 936 + 1872) / 30 = 188.07.

**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 1872 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872. So, factors of 1872 in pair are (1,1872), (2,936), (3,624), (4,468), (6,312), (8,234), (9,208), (12,156), (13,144), (16,117), (18,104), (24,78), (26,72), (36,52), (39,48).

Negative factors of 1872 are -1, -2, -3, -4, -6, -8, -9, -12, -13, -16, -18, -24, -26, -36, -39, -48, -52, -72, -78, -104, -117, -144, -156, -208, -234, -312, -468, -624, -936, -1872. Hence, factors of 1872 in pair are (-1,-1872), (-2,-936), (-3,-624), (-4,-468), (-6,-312), (-8,-234), (-9,-208), (-12,-156), (-13,-144), (-16,-117), (-18,-104), (-24,-78), (-26,-72), (-36,-52), (-39,-48).

Factors of 1872 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872. Positive factors of 1872 in pair are (1,1872), (2,936), (3,624), (4,468), (6,312), (8,234), (9,208), (12,156), (13,144), (16,117), (18,104), (24,78), (26,72), (36,52), (39,48). Negative factors of 1872 in pair are (-1,-1872), (-2,-936), (-3,-624), (-4,-468), (-6,-312), (-8,-234), (-9,-208), (-12,-156), (-13,-144), (-16,-117), (-18,-104), (-24,-78), (-26,-72), (-36,-52), (-39,-48).

Factors of 1872 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872. So the product of all factors of 1872 would be 1 x 2 x 3 x 4 x 6 x 8 x 9 x 12 x 13 x 16 x 18 x 24 x 26 x 36 x 39 x 48 x 52 x 72 x 78 x 104 x 117 x 144 x 156 x 208 x 234 x 312 x 468 x 624 x 936 x 1872 = 1.215031860223425e+49.

Factors of 1872 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872. Prime factors are 2, 2, 2, 2, 3, 3, 13. So, the product of all prime factors of 1872 would be 2 x 2 x 2 x 2 x 3 x 3 x 13 = 1872.

Factors of 1872 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872.

Factors of 1872 in pair are (1,1872), (2,936), (3,624), (4,468), (6,312), (8,234), (9,208), (12,156), (13,144), (16,117), (18,104), (24,78), (26,72), (36,52), (39,48).

To arrange 1872 blocks in all possible ways to form a rectangle, we need to calculate factors of 1872 in pair. Therefore, factors of 1872 in pair are (1,1872), (2,936), (3,624), (4,468), (6,312), (8,234), (9,208), (12,156), (13,144), (16,117), (18,104), (24,78), (26,72), (36,52), (39,48)