Steps to find Prime Factors of 17664 by Division Method

To find the primefactors of 17664 using the division method, follow these steps:

  • Step 1. Start dividing 17664 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 17664, which is 2. Divide 17664 by 2 to obtain the quotient (8832).
    17664 ÷ 2 = 8832
  • Step 3. Repeat step 1 with the obtained quotient (8832).
    8832 ÷ 2 = 4416
    4416 ÷ 2 = 2208
    2208 ÷ 2 = 1104
    1104 ÷ 2 = 552
    552 ÷ 2 = 276
    276 ÷ 2 = 138
    138 ÷ 2 = 69
    69 ÷ 3 = 23
    23 ÷ 23 = 1

So, the prime factorization of 17664 is, 17664 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 23.

Steps to find Prime Factors of 17664 by Factor Tree Method

We can follow the same procedure using the factor tree of 17664 as shown below:

So, the prime factorization of 17664 is, 17664 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 23.

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 17664 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 23.

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 17664 but not a prime factor of 17664.

Frequently Asked Questions

  • Which is the smallest prime factor of 17664?

    Smallest prime factor of 17664 is 2.

  • Is 17664 a perfect square?

    No 17664 is not a perfect square.

  • What is the prime factorization of 17664?

    Prime factorization of 17664 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 23.

  • What is prime factorization of 17664 in exponential form?

    Prime factorization of 17664 in exponential form is 28 x 3 x 23.

  • Is 17664 a prime number or a composite number?

    17664 is a composite number.

  • Which is the largest prime factors of 17664?

    The largest prime factor of 17664 is 23.

  • What is the product of all prime factors of 17664?

    Prime factors of 17664 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 23. Therefore, their product is 17664.

  • What numbers are the prime factors of 17664?

    Prime factors of 17664 are 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 23.

  • Is there any even prime factor of 17664?

    Yes there is a even prime factor of 17664.