Prime Factors of 1728

Steps to find Prime Factors of 1728 by Division Method

To find the primefactors of 1728 using the division method, follow these steps:

• Step 1. Start dividing 1728 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 1728, which is 2. Divide 1728 by 2 to obtain the quotient (864).
  1728 ÷ 2 = 864
• Step 3. Repeat step 1 with the obtained quotient (864).
  864 ÷ 2 = 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 1728 is, 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

Steps to find Prime Factors of 1728 by Factor Tree Method

We can follow the same procedure using the factor tree of 1728 as shown below:

So, the prime factorization of 1728 is, 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

What does Prime factor in mathematics mean?

Prime numbers, in mathematics are all those whole numbers greater than 1 having exactly two divisors that is 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 1728 are 2 x 2 x 2 x 2 x 2 x 2 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 1728 but not a prime factor of 1728.

Frequently Asked Questions

• Which is the smallest prime factor of 1728?

  Smallest prime factor of 1728 is 2.

• Is 1728 a perfect square?

  No 1728 is not a perfect square.

• What is the prime factorization of 1728?

  Prime factorization of 1728 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

• What is prime factorization of 1728 in exponential form?

  Prime factorization of 1728 in exponential form is 2⁶ x 3³.

• Is 1728 a prime number or a composite number?

  1728 is a composite number.

• Which is the largest prime factors of 1728?

  The largest prime factor of 1728 is 3.

• What is the product of all prime factors of 1728?

  Prime factors of 1728 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3. Therefore, their product is 1728.

• What numbers are the prime factors of 1728?

  Prime factors of 1728 are 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3.

• Is there any even prime factor of 1728?

  Yes there is a even prime factor of 1728.