Prime Factors of 459

Steps to find Prime Factors of 459 by Division Method

To find the primefactors of 459 using the division method, follow these steps:

• Step 1. Start dividing 459 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 459, which is 3. Divide 459 by 3 to obtain the quotient (153).
  459 ÷ 3 = 153
• Step 3. Repeat step 1 with the obtained quotient (153).
  153 ÷ 3 = 51
  51 ÷ 3 = 17
  17 ÷ 17 = 1

So, the prime factorization of 459 is, 459 = 3 x 3 x 3 x 17.

Steps to find Prime Factors of 459 by Factor Tree Method

We can follow the same procedure using the factor tree of 459 as shown below:

So, the prime factorization of 459 is, 459 = 3 x 3 x 3 x 17.

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 459 are 3 x 3 x 3 x 17.

Properties of Prime Factors

• For any given number there is one and only one set of unique prime factors.
• 2 is the only even prime number. So, any given number can have only one even prime factor and that is 2.
• Two prime factors of a given number are always coprime to each other.
• 1 is neither a prime number nor a composite number and also 1 is the factor of every given number. So, 1 is the factor of 459 but not a prime factor of 459.

Frequently Asked Questions

• Which is the smallest prime factor of 459?

  Smallest prime factor of 459 is 3.

• Is 459 a perfect square?

  No 459 is not a perfect square.

• What is the prime factorization of 459?

  Prime factorization of 459 is 3 x 3 x 3 x 17.

• What is prime factorization of 459 in exponential form?

  Prime factorization of 459 in exponential form is 3³ x 17.

• Is 459 a prime number?

  false, 459 is not a prime number.

• Which is the largest prime factors of 459?

  The largest prime factor of 459 is 17.

• What is the product of all prime factors of 459?

  Prime factors of 459 are 3 x 3 x 3 x 17. Therefore, their product is 459.

• What is the sum of all odd prime factors of 459?

  Prime factors of 459 are 3 , 3 , 3 , 17, out of which 3 , 3 , 3 , 17 are odd numbers. So, the sum of odd prime factors of 459 is 3 + 3 + 3 + 17 = 26.

• What is the product of all odd prime factors of 459?

  Prime factors of 459 are 3 , 3 , 3 , 17, out of which 3 , 3 , 3 , 17 are odd numbers. So, the product of odd prime factors of 459 is 3 x 3 x 3 x 17 = 459.