Factors of 864

2. Steps to find factors of 864 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 864 using the division method, follow these steps:

• Step 1. Start dividing 864 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 864, which is 2. Divide 864 by 2 to obtain the quotient (432).
  864 ÷ 2 = 432
• Step 3. Repeat step 1 with the obtained quotient (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 864 is, 864 = 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 864 as shown below:

So, the prime factorization of 864 is, 864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

3. Find factors of 864 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 864 would be the two numbers which, when multiplied, give 864 as the result.

The following table represents the calculation of factors of 864 in pairs:

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 864. They are called negative pair factors.

Hence, the negative pairs of 864 would be ( -1 , -864 ) , ( -2 , -432 ) , ( -3 , -288 ) , ( -4 , -216 ) , ( -6 , -144 ) , ( -8 , -108 ) , ( -9 , -96 ) , ( -12 , -72 ) , ( -16 , -54 ) , ( -18 , -48 ) , ( -24 , -36 ) and ( -27 , -32 ) .

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

Frequently Asked Questions

• Which is the smallest prime factor of 864?

  Smallest prime factor of 864 is 2.

• Is 864 a perfect square?

  No 864 is not a perfect square.

• What are five multiples of 864?

  First five multiples of 864 are 1728, 2592, 3456, 4320, 5184.

• What is prime factorization of 864?

  Prime factorization of 864 is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

• What are factors of 864?

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

• How do you find factors of a negative number? ( eg. -864 )?

  Factors of -864 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -72, -96, -108, -144, -216, -288, -432, -864.

• Is 864 a whole number?

  Yes 864 is a whole number.

• Which is greatest factor of 864?

  The greatest factor of 864 is 432.

• What are the prime factors of 864?

  The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864.
  Prime factors of 864 are 2, 2, 2, 2, 2, 3, 3, 3.

Examples of Factors