Prime Factors of 36864

Steps to find Prime Factors of 36864 by Division Method

To find the primefactors of 36864 using the division method, follow these steps:

• Step 1. Start dividing 36864 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 36864, which is 2. Divide 36864 by 2 to obtain the quotient (18432).
  36864 ÷ 2 = 18432
• Step 3. Repeat step 1 with the obtained quotient (18432).
  18432 ÷ 2 = 9216
  9216 ÷ 2 = 4608
  4608 ÷ 2 = 2304
  2304 ÷ 2 = 1152
  1152 ÷ 2 = 576
  576 ÷ 2 = 288
  288 ÷ 2 = 144
  144 ÷ 2 = 72
  72 ÷ 2 = 36
  36 ÷ 2 = 18
  18 ÷ 2 = 9
  9 ÷ 3 = 3
  3 ÷ 3 = 1

So, the prime factorization of 36864 is, 36864 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

Steps to find Prime Factors of 36864 by Factor Tree Method

We can follow the same procedure using the factor tree of 36864 as shown below:

So, the prime factorization of 36864 is, 36864 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

What does Prime factor of a number mean?

A prime number in mathematics is defined as any natural number greater than 1, that is not divisible by any number except 1 and the number itself. When we express any number as the product of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 36864 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

Properties of Prime Factors

• For any given number there is one and only one set of unique prime factors.
• Any number can have only 1 even prime factor and that is number 2.
• Two prime factors are always coprime to each other.
• 1 is the factor of any given number, but 1 is neither a prime number nor a composite number. So, 1 is the factor of 36864 but not a prime factor of 36864.

Frequently Asked Questions

• Which is the smallest prime factor of 36864?

  Smallest prime factor of 36864 is 2.

• Is 36864 a perfect square?

  Yes 36864 is a perfect square.

• What is the prime factorization of 36864?

  Prime factorization of 36864 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3.

• What is prime factorization of 36864 in exponential form?

  Prime factorization of 36864 in exponential form is 2¹² x 3².

• Is 36864 a prime number or a composite number?

  36864 is a composite number.

• Which is the largest prime factors of 36864?

  The largest prime factor of 36864 is 3.

• What is the product of all prime factors of 36864?

  Prime factors of 36864 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3. Therefore, their product is 36864.

• What numbers are the prime factors of 36864?

  Prime factors of 36864 are 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3.

• Is there any even prime factor of 36864?

  Yes there is a even prime factor of 36864.