Factors of 1575 in pair are (1, 1575) , (3, 525) , (5, 315) , (7, 225) , (9, 175) , (15, 105) , (21, 75) , (25, 63) and (35, 45)

- Find all the numbers that would divide 1575 without leaving any remainder. Starting with the number 1 upto 787 (half of 1575). The number 1 and the number itself are always factors of the given number.
- Pair the factors so that their product is 1575, and read off the answer!

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

1 and 1575 | 1 x 1575 = 1575 |

3 and 525 | 3 x 525 = 1575 |

5 and 315 | 5 x 315 = 1575 |

7 and 225 | 7 x 225 = 1575 |

9 and 175 | 9 x 175 = 1575 |

15 and 105 | 15 x 105 = 1575 |

21 and 75 | 21 x 75 = 1575 |

25 and 63 | 25 x 63 = 1575 |

35 and 45 | 35 x 45 = 1575 |

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 1575. They are called negative pair factors.

Hence, the negative pairs of 1575 would be ( -1 , -1575 ) .

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 1575 are 1 , 3 , 5 , 7 , 9 , 15 , 21 , 25 , 35 , 45 , 63 , 75 , 105 , 175 , 225 , 315 , 525 , 1575. So, factors of 1575 in pair are (1,1575), (3,525), (5,315), (7,225), (9,175), (15,105), (21,75), (25,63), (35,45).

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.

- Every number is a factor of zero (0), since 1575 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, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575 are exact divisors of 1575.
- Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. Each factor divides 1575 without leaving a remainder.

**Step 1.**Find all the numbers that would divide 1575 without leaving any remainder. Starting with the number 1 upto 787 (half of 1575). The number 1 and the number itself are always factors of the given number.1575 ÷ 1 : Remainder = 01575 ÷ 3 : Remainder = 01575 ÷ 5 : Remainder = 01575 ÷ 7 : Remainder = 01575 ÷ 9 : Remainder = 01575 ÷ 15 : Remainder = 01575 ÷ 21 : Remainder = 01575 ÷ 25 : Remainder = 01575 ÷ 35 : Remainder = 01575 ÷ 45 : Remainder = 01575 ÷ 63 : Remainder = 01575 ÷ 75 : Remainder = 01575 ÷ 105 : Remainder = 01575 ÷ 175 : Remainder = 01575 ÷ 225 : Remainder = 01575 ÷ 315 : Remainder = 01575 ÷ 525 : Remainder = 01575 ÷ 1575 : Remainder = 0

Hence, Factors of
*1575* are **1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, and 1575**

**Is 1575 a composite number?**Yes 1575 is a composite number.

**Is 1575 a perfect square?**No 1575 is not a perfect square.

**Write all odd factors of 1575?**The factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.

Odd factors of 1575 are 1 , 3 , 5 , 7 , 9 , 15 , 21 , 25 , 35 , 45 , 63 , 75 , 105 , 175 , 225 , 315 , 525 , 1575.**What is the mean of all prime factors of 1575?**Factors of 1575 are 1 , 3 , 5 , 7 , 9 , 15 , 21 , 25 , 35 , 45 , 63 , 75 , 105 , 175 , 225 , 315 , 525 , 1575. Prime factors of 1575 are 3 , 3 , 5 , 5 , 7. Therefore mean of prime factors of 1575 is (3 + 3 + 5 + 5 + 7) / 5 = 4.60.

**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.

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. Hence, the factors of 1575 in pair are (1,1575), (3,525), (5,315), (7,225), (9,175), (15,105), (21,75), (25,63), (35,45). Therefore, in total 9 pairs of factors are possible.

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. Positive factors of 1575 in pair are (1,1575), (3,525), (5,315), (7,225), (9,175), (15,105), (21,75), (25,63), (35,45). Negative factors of 1575 in pair are (-1,-1575), (-3,-525), (-5,-315), (-7,-225), (-9,-175), (-15,-105), (-21,-75), (-25,-63), (-35,-45).

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. So the product of all factors of 1575 would be 1 x 3 x 5 x 7 x 9 x 15 x 21 x 25 x 35 x 45 x 63 x 75 x 105 x 175 x 225 x 315 x 525 x 1575 = 5.963826811543969e+28.

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. Prime factors are 3, 3, 5, 5, 7. So, the product of all prime factors of 1575 would be 3 x 3 x 5 x 5 x 7 = 1575.

- Finding out all positive factors of 1575.

- Writing all prime factors of 1575.

- Writing all the possible factors of 1575 in pair.

Help him in writing all these.

Positive factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.

Prime factors of 1575 are 3, 3, 5, 5, 7.

Factors of 1575 in pair are (1,1575), (3,525), (5,315), (7,225), (9,175), (15,105), (21,75), (25,63), (35,45).

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. Hence, the factors of 1575 in pair are (1,1575), (3,525), (5,315), (7,225), (9,175), (15,105), (21,75), (25,63), (35,45).

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.

Factors of 1575 in pair are (1,1575), (3,525), (5,315), (7,225), (9,175), (15,105), (21,75), (25,63), (35,45).

To arrange 1575 blocks in all possible ways to form a rectangle, we need to calculate factors of 1575 in pair. Therefore, factors of 1575 in pair are (1,1575), (3,525), (5,315), (7,225), (9,175), (15,105), (21,75), (25,63), (35,45)