# Factors of 1728 in pair

Factors of 1728 in pair are (1, 1728) , (2, 864) , (3, 576) , (4, 432) , (6, 288) , (8, 216) , (9, 192) , (12, 144) , (16, 108) , (18, 96) , (24, 72) , (27, 64) , (32, 54) and (36, 48)

#### How to find factors of a number in pair

 1.   Steps to find factors of 1728 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 1728 in pair

Factor Pair Pair Factorization
1 and 1728 1 x 1728 = 1728
2 and 864 2 x 864 = 1728
3 and 576 3 x 576 = 1728
4 and 432 4 x 432 = 1728
6 and 288 6 x 288 = 1728
8 and 216 8 x 216 = 1728
9 and 192 9 x 192 = 1728
12 and 144 12 x 144 = 1728
16 and 108 16 x 108 = 1728
18 and 96 18 x 96 = 1728
24 and 72 24 x 72 = 1728
27 and 64 27 x 64 = 1728
32 and 54 32 x 54 = 1728
36 and 48 36 x 48 = 1728

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 1728. They are called negative pair factors.

Hence, the negative pairs of 1728 would be ( -1 , -1728 ) .

#### What does factor pairs in mathematics mean?

In mathematics, factor pair of a number are all those possible combination which when multiplied together give the original number in return. Every natural number is a product of atleast one factor pair. Eg- Factors of 1728 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 16 , 18 , 24 , 27 , 32 , 36 , 48 , 54 , 64 , 72 , 96 , 108 , 144 , 192 , 216 , 288 , 432 , 576 , 864 , 1728. So, factors of 1728 in pair are (1,1728), (2,864), (3,576), (4,432), (6,288), (8,216), (9,192), (12,144), (16,108), (18,96), (24,72), (27,64), (32,54), (36,48).

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 1728 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1728.
• Every number is a factor of zero (0), since 1728 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, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728 are exact divisors of 1728.
• Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. Each factor divides 1728 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, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728 are all less than or equal to 1728.

#### Steps to find Factors of 1728

• Step 1. Find all the numbers that would divide 1728 without leaving any remainder. Starting with the number 1 upto 864 (half of 1728). The number 1 and the number itself are always factors of the given number.
1728 ÷ 1 : Remainder = 0
1728 ÷ 2 : Remainder = 0
1728 ÷ 3 : Remainder = 0
1728 ÷ 4 : Remainder = 0
1728 ÷ 6 : Remainder = 0
1728 ÷ 8 : Remainder = 0
1728 ÷ 9 : Remainder = 0
1728 ÷ 12 : Remainder = 0
1728 ÷ 16 : Remainder = 0
1728 ÷ 18 : Remainder = 0
1728 ÷ 24 : Remainder = 0
1728 ÷ 27 : Remainder = 0
1728 ÷ 32 : Remainder = 0
1728 ÷ 36 : Remainder = 0
1728 ÷ 48 : Remainder = 0
1728 ÷ 54 : Remainder = 0
1728 ÷ 64 : Remainder = 0
1728 ÷ 72 : Remainder = 0
1728 ÷ 96 : Remainder = 0
1728 ÷ 108 : Remainder = 0
1728 ÷ 144 : Remainder = 0
1728 ÷ 192 : Remainder = 0
1728 ÷ 216 : Remainder = 0
1728 ÷ 288 : Remainder = 0
1728 ÷ 432 : Remainder = 0
1728 ÷ 576 : Remainder = 0
1728 ÷ 864 : Remainder = 0
1728 ÷ 1728 : Remainder = 0

Hence, Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, and 1728

#### Frequently Asked Questions

• Is 1728 a composite number?

Yes 1728 is a composite number.

• Is 1728 a prime number?

No 1728 is not a prime number.

• What is the mean of factors of 1728?

Factors of 1728 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 16 , 18 , 24 , 27 , 32 , 36 , 48 , 54 , 64 , 72 , 96 , 108 , 144 , 192 , 216 , 288 , 432 , 576 , 864 , 1728. therefore mean of factors of 1728 is (1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 96 + 108 + 144 + 192 + 216 + 288 + 432 + 576 + 864 + 1728) / 28 = 181.43.

• 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.

#### Examples of Factors

Ariel has been asked to write all factor pairs of 1728 but she is finding it difficult. Can you help her find out?

Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. So, factors of 1728 in pair are (1,1728), (2,864), (3,576), (4,432), (6,288), (8,216), (9,192), (12,144), (16,108), (18,96), (24,72), (27,64), (32,54), (36,48).

Sammy wants to write all the negative factors of 1728 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 1728 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -64, -72, -96, -108, -144, -192, -216, -288, -432, -576, -864, -1728. Hence, factors of 1728 in pair are (-1,-1728), (-2,-864), (-3,-576), (-4,-432), (-6,-288), (-8,-216), (-9,-192), (-12,-144), (-16,-108), (-18,-96), (-24,-72), (-27,-64), (-32,-54), (-36,-48).

Help Deep in writing the positive factors of 1728 in pair and negative factor of 1728 in pair.

Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. Positive factors of 1728 in pair are (1,1728), (2,864), (3,576), (4,432), (6,288), (8,216), (9,192), (12,144), (16,108), (18,96), (24,72), (27,64), (32,54), (36,48). Negative factors of 1728 in pair are (-1,-1728), (-2,-864), (-3,-576), (-4,-432), (-6,-288), (-8,-216), (-9,-192), (-12,-144), (-16,-108), (-18,-96), (-24,-72), (-27,-64), (-32,-54), (-36,-48).

Find the product of all factors of 1728.

Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. So the product of all factors of 1728 would be 1 x 2 x 3 x 4 x 6 x 8 x 9 x 12 x 16 x 18 x 24 x 27 x 32 x 36 x 48 x 54 x 64 x 72 x 96 x 108 x 144 x 192 x 216 x 288 x 432 x 576 x 864 x 1728 = 2.1164710578754843e+45.

Find the product of all prime factors of 1728.

Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. Prime factors are 2, 2, 2, 2, 2, 2, 3, 3, 3. So, the product of all prime factors of 1728 would be 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 = 1728.

Can you help Sammy list the factors of 1728 and also find the factor pairs?

Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728.
Factors of 1728 in pair are (1,1728), (2,864), (3,576), (4,432), (6,288), (8,216), (9,192), (12,144), (16,108), (18,96), (24,72), (27,64), (32,54), (36,48).

Sammy has 1728 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 1728 blocks in all possible ways to form a rectangle, we need to calculate factors of 1728 in pair. Therefore, factors of 1728 in pair are (1,1728), (2,864), (3,576), (4,432), (6,288), (8,216), (9,192), (12,144), (16,108), (18,96), (24,72), (27,64), (32,54), (36,48)

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