Prime Factors of 46656

Steps to find Prime Factors of 46656 by Division Method

To find the primefactors of 46656 using the division method, follow these steps:

• Step 1. Start dividing 46656 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 46656, which is 2. Divide 46656 by 2 to obtain the quotient (23328).
  46656 ÷ 2 = 23328
• Step 3. Repeat step 1 with the obtained quotient (23328).
  23328 ÷ 2 = 11664
  11664 ÷ 2 = 5832
  5832 ÷ 2 = 2916
  2916 ÷ 2 = 1458
  1458 ÷ 2 = 729
  729 ÷ 3 = 243
  243 ÷ 3 = 81
  81 ÷ 3 = 27
  27 ÷ 3 = 9
  9 ÷ 3 = 3
  3 ÷ 3 = 1

So, the prime factorization of 46656 is, 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3.

Steps to find Prime Factors of 46656 by Factor Tree Method

We can follow the same procedure using the factor tree of 46656 as shown below:

So, the prime factorization of 46656 is, 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3.

Introduction to Prime Factors?

In mathematics, prime numbers are defined as all those natural numbers greater than 1 that has only two divisors one being number 1 and the other being the number itself. When we express any number as the products of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 46656 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 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 46656 but not a prime factor of 46656.

Frequently Asked Questions

• Which is the smallest prime factor of 46656?

  Smallest prime factor of 46656 is 2.

• Is 46656 a perfect square?

  Yes 46656 is a perfect square.

• What is the prime factorization of 46656?

  Prime factorization of 46656 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3.

• What is prime factorization of 46656 in exponential form?

  Prime factorization of 46656 in exponential form is 2⁶ x 3⁶.

• Is 46656 a prime number or a composite number?

  46656 is a composite number.

• Which is the largest prime factors of 46656?

  The largest prime factor of 46656 is 3.

• What is the product of all prime factors of 46656?

  Prime factors of 46656 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3. Therefore, their product is 46656.

• What numbers are the prime factors of 46656?

  Prime factors of 46656 are 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3.

• Is there any even prime factor of 46656?

  Yes there is a even prime factor of 46656.