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

How to find factors of a number

1. Steps to find factors of 1728 using Division Method

Example: Find factors of 1728

  • Divide 1728 by 1: 1728 ÷ 1 : Remainder = 0
  • Divide 1728 by 2: 1728 ÷ 2 : Remainder = 0
  • Divide 1728 by 3: 1728 ÷ 3 : Remainder = 0
  • Divide 1728 by 4: 1728 ÷ 4 : Remainder = 0
  • Divide 1728 by 6: 1728 ÷ 6 : Remainder = 0
  • Divide 1728 by 8: 1728 ÷ 8 : Remainder = 0
  • Divide 1728 by 9: 1728 ÷ 9 : Remainder = 0
  • Divide 1728 by 12: 1728 ÷ 12 : Remainder = 0
  • Divide 1728 by 16: 1728 ÷ 16 : Remainder = 0
  • Divide 1728 by 18: 1728 ÷ 18 : Remainder = 0
  • Divide 1728 by 24: 1728 ÷ 24 : Remainder = 0
  • Divide 1728 by 27: 1728 ÷ 27 : Remainder = 0
  • Divide 1728 by 32: 1728 ÷ 32 : Remainder = 0
  • Divide 1728 by 36: 1728 ÷ 36 : Remainder = 0
  • Divide 1728 by 48: 1728 ÷ 48 : Remainder = 0
  • Divide 1728 by 54: 1728 ÷ 54 : Remainder = 0
  • Divide 1728 by 64: 1728 ÷ 64 : Remainder = 0
  • Divide 1728 by 72: 1728 ÷ 72 : Remainder = 0
  • Divide 1728 by 96: 1728 ÷ 96 : Remainder = 0
  • Divide 1728 by 108: 1728 ÷ 108 : Remainder = 0
  • Divide 1728 by 144: 1728 ÷ 144 : Remainder = 0
  • Divide 1728 by 192: 1728 ÷ 192 : Remainder = 0
  • Divide 1728 by 216: 1728 ÷ 216 : Remainder = 0
  • Divide 1728 by 288: 1728 ÷ 288 : Remainder = 0
  • Divide 1728 by 432: 1728 ÷ 432 : Remainder = 0
  • Divide 1728 by 576: 1728 ÷ 576 : Remainder = 0
  • Divide 1728 by 864: 1728 ÷ 864 : Remainder = 0
  • Divide 1728 by 1728: 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

2. Steps to find factors of 1728 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 1728 using the division method, follow these steps:

  • Step 1. Start dividing 1728 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 1728, which is 2. Divide 1728 by 2 to obtain the quotient (864).
    1728 ÷ 2 = 864
  • Step 3. Repeat step 1 with the obtained quotient (864).
    864 ÷ 2 = 432
    432 ÷ 2 = 216
    216 ÷ 2 = 108
    108 ÷ 2 = 54
    54 ÷ 2 = 27
    27 ÷ 3 = 9
    9 ÷ 3 = 3
    3 ÷ 3 = 1

So, the prime factorization of 1728 is, 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1728 as shown below:

So, the prime factorization of 1728 is, 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

3. Find factors of 1728 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1728 would be the two numbers which, when multiplied, give 1728 as the result.

The following table represents the calculation of factors of 1728 in pairs:

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 ) , ( -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 ) .

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.

Frequently Asked Questions

  • Which is the smallest prime factor of 1728?

    Smallest prime factor of 1728 is 2.

  • Is 1728 a perfect square?

    No 1728 is not a perfect square.

  • What are five multiples of 1728?

    First five multiples of 1728 are 3456, 5184, 6912, 8640, 10368.

  • What is prime factorization of 1728?

    Prime factorization of 1728 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

  • What are 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.

  • How do you find factors of a negative number? ( eg. -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.

  • Is 1728 a whole number?

    Yes 1728 is a whole number.

  • Which is greatest factor of 1728?

    The greatest factor of 1728 is 864.

  • What are the prime factors of 1728?

    The 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 of 1728 are 2, 2, 2, 2, 2, 2, 3, 3, 3.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1728. Can you help her?

Prime factors of 1728 are 2, 2, 2, 2, 2, 2, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even 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.
Even factors of 1728 are 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728.
Hence, product of even factors of 1728 is; 2 x 4 x 6 x 8 x 12 x 16 x 18 x 24 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 = 2.9032524799389365e+42.

Joy wants to calculate mean of all the factors of 1728. Help him in finding the mean 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.
To calculate the mean we need to calculate the sum of factors first. Sum 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 = 5080.
Hence, the mean of factors of 1728 is 5080 ÷ 28 = 181.43.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1728? Help her in writing all the factors.

Positive factors 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.
Negative factors 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.

How many factors are there for 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 there are in total 28 factors.

Joey wants to write all the prime factors of 1728 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1728 are 2, 2, 2, 2, 2, 2, 3, 3, 3.
So in exponential form it can be written as 26 x 33.

Kevin has been asked to write 27 factor(s) of 1728. Can you predict the answer?

27 factor(s) 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.