Factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, and 13824

How to find factors of a number

1. Steps to find factors of 13824 using Division Method

Example: Find factors of 13824

  • Divide 13824 by 1: 13824 ÷ 1 : Remainder = 0
  • Divide 13824 by 2: 13824 ÷ 2 : Remainder = 0
  • Divide 13824 by 3: 13824 ÷ 3 : Remainder = 0
  • Divide 13824 by 4: 13824 ÷ 4 : Remainder = 0
  • Divide 13824 by 6: 13824 ÷ 6 : Remainder = 0
  • Divide 13824 by 8: 13824 ÷ 8 : Remainder = 0
  • Divide 13824 by 9: 13824 ÷ 9 : Remainder = 0
  • Divide 13824 by 12: 13824 ÷ 12 : Remainder = 0
  • Divide 13824 by 16: 13824 ÷ 16 : Remainder = 0
  • Divide 13824 by 18: 13824 ÷ 18 : Remainder = 0
  • Divide 13824 by 24: 13824 ÷ 24 : Remainder = 0
  • Divide 13824 by 27: 13824 ÷ 27 : Remainder = 0
  • Divide 13824 by 32: 13824 ÷ 32 : Remainder = 0
  • Divide 13824 by 36: 13824 ÷ 36 : Remainder = 0
  • Divide 13824 by 48: 13824 ÷ 48 : Remainder = 0
  • Divide 13824 by 54: 13824 ÷ 54 : Remainder = 0
  • Divide 13824 by 64: 13824 ÷ 64 : Remainder = 0
  • Divide 13824 by 72: 13824 ÷ 72 : Remainder = 0
  • Divide 13824 by 96: 13824 ÷ 96 : Remainder = 0
  • Divide 13824 by 108: 13824 ÷ 108 : Remainder = 0
  • Divide 13824 by 128: 13824 ÷ 128 : Remainder = 0
  • Divide 13824 by 144: 13824 ÷ 144 : Remainder = 0
  • Divide 13824 by 192: 13824 ÷ 192 : Remainder = 0
  • Divide 13824 by 216: 13824 ÷ 216 : Remainder = 0
  • Divide 13824 by 256: 13824 ÷ 256 : Remainder = 0
  • Divide 13824 by 288: 13824 ÷ 288 : Remainder = 0
  • Divide 13824 by 384: 13824 ÷ 384 : Remainder = 0
  • Divide 13824 by 432: 13824 ÷ 432 : Remainder = 0
  • Divide 13824 by 512: 13824 ÷ 512 : Remainder = 0
  • Divide 13824 by 576: 13824 ÷ 576 : Remainder = 0
  • Divide 13824 by 768: 13824 ÷ 768 : Remainder = 0
  • Divide 13824 by 864: 13824 ÷ 864 : Remainder = 0
  • Divide 13824 by 1152: 13824 ÷ 1152 : Remainder = 0
  • Divide 13824 by 1536: 13824 ÷ 1536 : Remainder = 0
  • Divide 13824 by 1728: 13824 ÷ 1728 : Remainder = 0
  • Divide 13824 by 2304: 13824 ÷ 2304 : Remainder = 0
  • Divide 13824 by 3456: 13824 ÷ 3456 : Remainder = 0
  • Divide 13824 by 4608: 13824 ÷ 4608 : Remainder = 0
  • Divide 13824 by 6912: 13824 ÷ 6912 : Remainder = 0
  • Divide 13824 by 13824: 13824 ÷ 13824 : Remainder = 0

Hence, Factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, and 13824

2. Steps to find factors of 13824 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 13824 using the division method, follow these steps:

  • Step 1. Start dividing 13824 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 13824, which is 2. Divide 13824 by 2 to obtain the quotient (6912).
    13824 ÷ 2 = 6912
  • Step 3. Repeat step 1 with the obtained quotient (6912).
    6912 ÷ 2 = 3456
    3456 ÷ 2 = 1728
    1728 ÷ 2 = 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 13824 is, 13824 = 2 x 2 x 2 x 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 13824 as shown below:

So, the prime factorization of 13824 is, 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

3. Find factors of 13824 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 13824 would be the two numbers which, when multiplied, give 13824 as the result.

The following table represents the calculation of factors of 13824 in pairs:

Factor Pair Pair Factorization
1 and 13824 1 x 13824 = 13824
2 and 6912 2 x 6912 = 13824
3 and 4608 3 x 4608 = 13824
4 and 3456 4 x 3456 = 13824
6 and 2304 6 x 2304 = 13824
8 and 1728 8 x 1728 = 13824
9 and 1536 9 x 1536 = 13824
12 and 1152 12 x 1152 = 13824
16 and 864 16 x 864 = 13824
18 and 768 18 x 768 = 13824
24 and 576 24 x 576 = 13824
27 and 512 27 x 512 = 13824
32 and 432 32 x 432 = 13824
36 and 384 36 x 384 = 13824
48 and 288 48 x 288 = 13824
54 and 256 54 x 256 = 13824
64 and 216 64 x 216 = 13824
72 and 192 72 x 192 = 13824
96 and 144 96 x 144 = 13824
108 and 128 108 x 128 = 13824

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 13824. They are called negative pair factors.

Hence, the negative pairs of 13824 would be ( -1 , -13824 ) , ( -2 , -6912 ) , ( -3 , -4608 ) , ( -4 , -3456 ) , ( -6 , -2304 ) , ( -8 , -1728 ) , ( -9 , -1536 ) , ( -12 , -1152 ) , ( -16 , -864 ) , ( -18 , -768 ) , ( -24 , -576 ) , ( -27 , -512 ) , ( -32 , -432 ) , ( -36 , -384 ) , ( -48 , -288 ) , ( -54 , -256 ) , ( -64 , -216 ) , ( -72 , -192 ) , ( -96 , -144 ) and ( -108 , -128 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

  • Each number is a factor of itself. Eg. 13824 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 13824.
  • Every number is a factor of zero (0), since 13824 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, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824 are exact divisors of 13824.
  • Factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824. Each factor divides 13824 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, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824 are all less than or equal to 13824.

Frequently Asked Questions

  • Which is the smallest prime factor of 13824?

    Smallest prime factor of 13824 is 2.

  • Is 13824 a perfect square?

    No 13824 is not a perfect square.

  • What are five multiples of 13824?

    First five multiples of 13824 are 27648, 41472, 55296, 69120, 82944.

  • What is prime factorization of 13824?

    Prime factorization of 13824 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

  • What are factors of 13824?

    Factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824.

  • How do you find factors of a negative number? ( eg. -13824 )?

    Factors of -13824 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -64, -72, -96, -108, -128, -144, -192, -216, -256, -288, -384, -432, -512, -576, -768, -864, -1152, -1536, -1728, -2304, -3456, -4608, -6912, -13824.

  • Is 13824 a whole number?

    Yes 13824 is a whole number.

  • Which is greatest factor of 13824?

    The greatest factor of 13824 is 6912.

  • What are the prime factors of 13824?

    The factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824.
    Prime factors of 13824 are 2, 2, 2, 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 13824. Can you help her?

Prime factors of 13824 are 2, 2, 2, 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 13824?

Factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824.
Even factors of 13824 are 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824.
Hence, product of even factors of 13824 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 128 x 144 x 192 x 216 x 256 x 288 x 384 x 432 x 512 x 576 x 768 x 864 x 1152 x 1536 x 1728 x 2304 x 3456 x 4608 x 6912 x 13824 = 8.911421265968306e+79.

Joy wants to calculate mean of all the factors of 13824. Help him in finding the mean of 13824.

Factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 13824 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 96 + 108 + 128 + 144 + 192 + 216 + 256 + 288 + 384 + 432 + 512 + 576 + 768 + 864 + 1152 + 1536 + 1728 + 2304 + 3456 + 4608 + 6912 + 13824 = 40920.
Hence, the mean of factors of 13824 is 40920 ÷ 40 = 1023.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 13824? 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, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -64, -72, -96, -108, -128, -144, -192, -216, -256, -288, -384, -432, -512, -576, -768, -864, -1152, -1536, -1728, -2304, -3456, -4608, -6912, -13824.

How many factors are there for 13824?

Factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824.
So there are in total 40 factors.

Joey wants to write all the prime factors of 13824 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 13824 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3.
So in exponential form it can be written as 29 x 33.

Kevin has been asked to write 39 factor(s) of 13824. Can you predict the answer?

39 factor(s) of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912.