Factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, and 5184

How to find factors of a number

1. Steps to find factors of 5184 using Division Method

Example: Find factors of 5184

  • Divide 5184 by 1: 5184 ÷ 1 : Remainder = 0
  • Divide 5184 by 2: 5184 ÷ 2 : Remainder = 0
  • Divide 5184 by 3: 5184 ÷ 3 : Remainder = 0
  • Divide 5184 by 4: 5184 ÷ 4 : Remainder = 0
  • Divide 5184 by 6: 5184 ÷ 6 : Remainder = 0
  • Divide 5184 by 8: 5184 ÷ 8 : Remainder = 0
  • Divide 5184 by 9: 5184 ÷ 9 : Remainder = 0
  • Divide 5184 by 12: 5184 ÷ 12 : Remainder = 0
  • Divide 5184 by 16: 5184 ÷ 16 : Remainder = 0
  • Divide 5184 by 18: 5184 ÷ 18 : Remainder = 0
  • Divide 5184 by 24: 5184 ÷ 24 : Remainder = 0
  • Divide 5184 by 27: 5184 ÷ 27 : Remainder = 0
  • Divide 5184 by 32: 5184 ÷ 32 : Remainder = 0
  • Divide 5184 by 36: 5184 ÷ 36 : Remainder = 0
  • Divide 5184 by 48: 5184 ÷ 48 : Remainder = 0
  • Divide 5184 by 54: 5184 ÷ 54 : Remainder = 0
  • Divide 5184 by 64: 5184 ÷ 64 : Remainder = 0
  • Divide 5184 by 72: 5184 ÷ 72 : Remainder = 0
  • Divide 5184 by 81: 5184 ÷ 81 : Remainder = 0
  • Divide 5184 by 96: 5184 ÷ 96 : Remainder = 0
  • Divide 5184 by 108: 5184 ÷ 108 : Remainder = 0
  • Divide 5184 by 144: 5184 ÷ 144 : Remainder = 0
  • Divide 5184 by 162: 5184 ÷ 162 : Remainder = 0
  • Divide 5184 by 192: 5184 ÷ 192 : Remainder = 0
  • Divide 5184 by 216: 5184 ÷ 216 : Remainder = 0
  • Divide 5184 by 288: 5184 ÷ 288 : Remainder = 0
  • Divide 5184 by 324: 5184 ÷ 324 : Remainder = 0
  • Divide 5184 by 432: 5184 ÷ 432 : Remainder = 0
  • Divide 5184 by 576: 5184 ÷ 576 : Remainder = 0
  • Divide 5184 by 648: 5184 ÷ 648 : Remainder = 0
  • Divide 5184 by 864: 5184 ÷ 864 : Remainder = 0
  • Divide 5184 by 1296: 5184 ÷ 1296 : Remainder = 0
  • Divide 5184 by 1728: 5184 ÷ 1728 : Remainder = 0
  • Divide 5184 by 2592: 5184 ÷ 2592 : Remainder = 0
  • Divide 5184 by 5184: 5184 ÷ 5184 : Remainder = 0

Hence, Factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, and 5184

2. Steps to find factors of 5184 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 5184 using the division method, follow these steps:

  • Step 1. Start dividing 5184 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 5184, which is 2. Divide 5184 by 2 to obtain the quotient (2592).
    5184 ÷ 2 = 2592
  • Step 3. Repeat step 1 with the obtained quotient (2592).
    2592 ÷ 2 = 1296
    1296 ÷ 2 = 648
    648 ÷ 2 = 324
    324 ÷ 2 = 162
    162 ÷ 2 = 81
    81 ÷ 3 = 27
    27 ÷ 3 = 9
    9 ÷ 3 = 3
    3 ÷ 3 = 1

So, the prime factorization of 5184 is, 5184 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 5184 as shown below:

So, the prime factorization of 5184 is, 5184 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3.

3. Find factors of 5184 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 5184 would be the two numbers which, when multiplied, give 5184 as the result.

The following table represents the calculation of factors of 5184 in pairs:

Factor Pair Pair Factorization
1 and 5184 1 x 5184 = 5184
2 and 2592 2 x 2592 = 5184
3 and 1728 3 x 1728 = 5184
4 and 1296 4 x 1296 = 5184
6 and 864 6 x 864 = 5184
8 and 648 8 x 648 = 5184
9 and 576 9 x 576 = 5184
12 and 432 12 x 432 = 5184
16 and 324 16 x 324 = 5184
18 and 288 18 x 288 = 5184
24 and 216 24 x 216 = 5184
27 and 192 27 x 192 = 5184
32 and 162 32 x 162 = 5184
36 and 144 36 x 144 = 5184
48 and 108 48 x 108 = 5184
54 and 96 54 x 96 = 5184
64 and 81 64 x 81 = 5184
72 and 72 72 x 72 = 5184

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 5184. They are called negative pair factors.

Hence, the negative pairs of 5184 would be ( -1 , -5184 ) , ( -2 , -2592 ) , ( -3 , -1728 ) , ( -4 , -1296 ) , ( -6 , -864 ) , ( -8 , -648 ) , ( -9 , -576 ) , ( -12 , -432 ) , ( -16 , -324 ) , ( -18 , -288 ) , ( -24 , -216 ) , ( -27 , -192 ) , ( -32 , -162 ) , ( -36 , -144 ) , ( -48 , -108 ) , ( -54 , -96 ) , ( -64 , -81 ) and ( -72 , -72 ) .

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. 5184 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 5184.
  • Every number is a factor of zero (0), since 5184 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, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184 are exact divisors of 5184.
  • Factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184. Each factor divides 5184 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, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184 are all less than or equal to 5184.

Frequently Asked Questions

  • Which is the smallest prime factor of 5184?

    Smallest prime factor of 5184 is 2.

  • Is 5184 a perfect square?

    Yes 5184 is a perfect square.

  • What are five multiples of 5184?

    First five multiples of 5184 are 10368, 15552, 20736, 25920, 31104.

  • What is prime factorization of 5184?

    Prime factorization of 5184 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3.

  • What are factors of 5184?

    Factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.

  • How do you find factors of a negative number? ( eg. -5184 )?

    Factors of -5184 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -64, -72, -81, -96, -108, -144, -162, -192, -216, -288, -324, -432, -576, -648, -864, -1296, -1728, -2592, -5184.

  • Is 5184 a whole number?

    Yes 5184 is a whole number.

  • Which is greatest factor of 5184?

    The greatest factor of 5184 is 2592.

  • What are the prime factors of 5184?

    The factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.
    Prime factors of 5184 are 2, 2, 2, 2, 2, 2, 3, 3, 3, 3.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 5184. Can you help her?

Prime factors of 5184 are 2, 2, 2, 2, 2, 2, 3, 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 5184?

Factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.
Even factors of 5184 are 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 64, 72, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.
Hence, product of even factors of 5184 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 162 x 192 x 216 x 288 x 324 x 432 x 576 x 648 x 864 x 1296 x 1728 x 2592 x 5184 = 1.7195896714223262e+60.

Joy wants to calculate mean of all the factors of 5184. Help him in finding the mean of 5184.

Factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 5184 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 81 + 96 + 108 + 144 + 162 + 192 + 216 + 288 + 324 + 432 + 576 + 648 + 864 + 1296 + 1728 + 2592 + 5184 = 15367.
Hence, the mean of factors of 5184 is 15367 ÷ 35 = 439.06.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 5184? 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, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -64, -72, -81, -96, -108, -144, -162, -192, -216, -288, -324, -432, -576, -648, -864, -1296, -1728, -2592, -5184.

How many factors are there for 5184?

Factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.
So there are in total 35 factors.

Joey wants to write all the prime factors of 5184 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 5184 are 2, 2, 2, 2, 2, 2, 3, 3, 3, 3.
So in exponential form it can be written as 26 x 34.

Kevin has been asked to write 34 factor(s) of 5184. Can you predict the answer?

34 factor(s) of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592.