Prime Factors of 1305

Steps to find Prime Factors of 1305 by Division Method

To find the primefactors of 1305 using the division method, follow these steps:

• Step 1. Start dividing 1305 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 1305, which is 3. Divide 1305 by 3 to obtain the quotient (435).
  1305 ÷ 3 = 435
• Step 3. Repeat step 1 with the obtained quotient (435).
  435 ÷ 3 = 145
  145 ÷ 5 = 29
  29 ÷ 29 = 1

So, the prime factorization of 1305 is, 1305 = 3 x 3 x 5 x 29.

Steps to find Prime Factors of 1305 by Factor Tree Method

We can follow the same procedure using the factor tree of 1305 as shown below:

So, the prime factorization of 1305 is, 1305 = 3 x 3 x 5 x 29.

Definition of Prime Factors?

In mathematics, prime numbers are defined as all those whole numbers greater than 1 that have only two factors, i.e. 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 1305 are 3 x 3 x 5 x 29.

Properties of Prime Factors

• Prime factors are the set of factors that are unique to the number given.
• 2 is the only even prime factor any number can have.
• Two prime factors 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 1305 but not a prime factor of 1305.

Frequently Asked Questions

• Which is the smallest prime factor of 1305?

  Smallest prime factor of 1305 is 3.

• What is the prime factorization of 1305?

  Prime factorization of 1305 is 3 x 3 x 5 x 29.

• What is prime factorization of 1305 in exponential form?

  Prime factorization of 1305 in exponential form is 3² x 5 x 29.

• Is 1305 a prime number or a composite number?

  1305 is a composite number.

• Is 1305 a prime number?

  false, 1305 is not a prime number.

• How to find prime factorization of 1305 easily?

  To find prime factorization of 1305 easily you can refer to the steps given on this page step by step.

• Which is the largest prime factors of 1305?

  The largest prime factor of 1305 is 29.

• What is the product of all prime factors of 1305?

  Prime factors of 1305 are 3 x 3 x 5 x 29. Therefore, their product is 1305.

• What is the sum of all odd prime factors of 1305?

  Prime factors of 1305 are 3 , 3 , 5 , 29, out of which 3 , 3 , 5 , 29 are odd numbers. So, the sum of odd prime factors of 1305 is 3 + 3 + 5 + 29 = 40.