Factors of 5292 in pair are (1, 5292) , (2, 2646) , (3, 1764) , (4, 1323) , (6, 882) , (7, 756) , (9, 588) , (12, 441) , (14, 378) , (18, 294) , (21, 252) , (27, 196) , (28, 189) , (36, 147) , (42, 126) , (49, 108) , (54, 98) and (63, 84)

- Find all the numbers that would divide 5292 without leaving any remainder. Starting with the number 1 upto 2646 (half of 5292). The number 1 and the number itself are always factors of the given number.
- Pair the factors so that their product is 5292, and read off the answer!

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

1 and 5292 | 1 x 5292 = 5292 |

2 and 2646 | 2 x 2646 = 5292 |

3 and 1764 | 3 x 1764 = 5292 |

4 and 1323 | 4 x 1323 = 5292 |

6 and 882 | 6 x 882 = 5292 |

7 and 756 | 7 x 756 = 5292 |

9 and 588 | 9 x 588 = 5292 |

12 and 441 | 12 x 441 = 5292 |

14 and 378 | 14 x 378 = 5292 |

18 and 294 | 18 x 294 = 5292 |

21 and 252 | 21 x 252 = 5292 |

27 and 196 | 27 x 196 = 5292 |

28 and 189 | 28 x 189 = 5292 |

36 and 147 | 36 x 147 = 5292 |

42 and 126 | 42 x 126 = 5292 |

49 and 108 | 49 x 108 = 5292 |

54 and 98 | 54 x 98 = 5292 |

63 and 84 | 63 x 84 = 5292 |

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 5292. They are called negative pair factors.

Hence, the negative pairs of 5292 would be ( -1 , -5292 ) .

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 5292 are 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 27 , 28 , 36 , 42 , 49 , 54 , 63 , 84 , 98 , 108 , 126 , 147 , 189 , 196 , 252 , 294 , 378 , 441 , 588 , 756 , 882 , 1323 , 1764 , 2646 , 5292. So, factors of 5292 in pair are (1,5292), (2,2646), (3,1764), (4,1323), (6,882), (7,756), (9,588), (12,441), (14,378), (18,294), (21,252), (27,196), (28,189), (36,147), (42,126), (49,108), (54,98), (63,84).

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. 5292 is a factor of itself.
- 1 is a factor of every number. Eg. 1 is a factor of 5292.
- Every number is a factor of zero (0), since 5292 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, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, 5292 are exact divisors of 5292.
- Factors of 5292 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, 5292. Each factor divides 5292 without leaving a remainder.
- Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, 5292 are all less than or equal to 5292.

**Step 1.**Find all the numbers that would divide 5292 without leaving any remainder. Starting with the number 1 upto 2646 (half of 5292). The number 1 and the number itself are always factors of the given number.5292 ÷ 1 : Remainder = 05292 ÷ 2 : Remainder = 05292 ÷ 3 : Remainder = 05292 ÷ 4 : Remainder = 05292 ÷ 6 : Remainder = 05292 ÷ 7 : Remainder = 05292 ÷ 9 : Remainder = 05292 ÷ 12 : Remainder = 05292 ÷ 14 : Remainder = 05292 ÷ 18 : Remainder = 05292 ÷ 21 : Remainder = 05292 ÷ 27 : Remainder = 05292 ÷ 28 : Remainder = 05292 ÷ 36 : Remainder = 05292 ÷ 42 : Remainder = 05292 ÷ 49 : Remainder = 05292 ÷ 54 : Remainder = 05292 ÷ 63 : Remainder = 05292 ÷ 84 : Remainder = 05292 ÷ 98 : Remainder = 05292 ÷ 108 : Remainder = 05292 ÷ 126 : Remainder = 05292 ÷ 147 : Remainder = 05292 ÷ 189 : Remainder = 05292 ÷ 196 : Remainder = 05292 ÷ 252 : Remainder = 05292 ÷ 294 : Remainder = 05292 ÷ 378 : Remainder = 05292 ÷ 441 : Remainder = 05292 ÷ 588 : Remainder = 05292 ÷ 756 : Remainder = 05292 ÷ 882 : Remainder = 05292 ÷ 1323 : Remainder = 05292 ÷ 1764 : Remainder = 05292 ÷ 2646 : Remainder = 05292 ÷ 5292 : Remainder = 0

Hence, Factors of
*5292* are **1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, and 5292**

**Is 5292 a composite number?**Yes 5292 is a composite number.

**Is 5292 a prime number?**No 5292 is not a prime number.

**What is the mean of factors of 5292?**Factors of 5292 are 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 27 , 28 , 36 , 42 , 49 , 54 , 63 , 84 , 98 , 108 , 126 , 147 , 189 , 196 , 252 , 294 , 378 , 441 , 588 , 756 , 882 , 1323 , 1764 , 2646 , 5292. therefore mean of factors of 5292 is (1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 27 + 28 + 36 + 42 + 49 + 54 + 63 + 84 + 98 + 108 + 126 + 147 + 189 + 196 + 252 + 294 + 378 + 441 + 588 + 756 + 882 + 1323 + 1764 + 2646 + 5292) / 36 = 443.33.

**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 5292.

- Writing all prime factors of 5292.

- Writing all the possible factors of 5292 in pair.

Help him in writing all these.

Positive factors of 5292 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, 5292.

Prime factors of 5292 are 2, 2, 3, 3, 3, 7, 7.

Factors of 5292 in pair are (1,5292), (2,2646), (3,1764), (4,1323), (6,882), (7,756), (9,588), (12,441), (14,378), (18,294), (21,252), (27,196), (28,189), (36,147), (42,126), (49,108), (54,98), (63,84).

Factors of 5292 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, 5292. Hence, the factors of 5292 in pair are (1,5292), (2,2646), (3,1764), (4,1323), (6,882), (7,756), (9,588), (12,441), (14,378), (18,294), (21,252), (27,196), (28,189), (36,147), (42,126), (49,108), (54,98), (63,84).

Factors of 5292 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, 5292.

Factors of 5292 in pair are (1,5292), (2,2646), (3,1764), (4,1323), (6,882), (7,756), (9,588), (12,441), (14,378), (18,294), (21,252), (27,196), (28,189), (36,147), (42,126), (49,108), (54,98), (63,84).

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 5292 in pair. So, the possible combinations (1,5292), (2,2646), (3,1764), (4,1323), (6,882), (7,756), (9,588), (12,441), (14,378), (18,294), (21,252), (27,196), (28,189), (36,147), (42,126), (49,108), (54,98), (63,84).

Prime factorization of 5292 is 2 x 2 x 3 x 3 x 3 x 7 x 7. Factors of 5292 in pair can be written as (1,5292), (2,2646), (3,1764), (4,1323), (6,882), (7,756), (9,588), (12,441), (14,378), (18,294), (21,252), (27,196), (28,189), (36,147), (42,126), (49,108), (54,98), (63,84).

Smallest prime factor of 5292 is 2.

Largest prime factor of 5292 is 7.

Negative factors of 5292 are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -27, -28, -36, -42, -49, -54, -63, -84, -98, -108, -126, -147, -189, -196, -252, -294, -378, -441, -588, -756, -882, -1323, -1764, -2646, -5292.