# Prime Factors of 17664

Prime Factors of 17664 are 2, 2, 2, 2, 2, 2, 2, 2, 3, and 23

#### How to find prime factors of a number

 1.   Prime Factorization of 17664 by Division Method 2.   Prime Factorization of 17664 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### 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.

• 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.