Prime Factors of 735

Steps to find Prime Factors of 735 by Division Method

To find the primefactors of 735 using the division method, follow these steps:

• Step 1. Start dividing 735 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 735, which is 3. Divide 735 by 3 to obtain the quotient (245).
  735 ÷ 3 = 245
• Step 3. Repeat step 1 with the obtained quotient (245).
  245 ÷ 5 = 49
  49 ÷ 7 = 7
  7 ÷ 7 = 1

So, the prime factorization of 735 is, 735 = 3 x 5 x 7 x 7.

Steps to find Prime Factors of 735 by Factor Tree Method

We can follow the same procedure using the factor tree of 735 as shown below:

So, the prime factorization of 735 is, 735 = 3 x 5 x 7 x 7.

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 735 are 3 x 5 x 7 x 7.

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 735 but not a prime factor of 735.

Frequently Asked Questions

• Which is the smallest prime factor of 735?

  Smallest prime factor of 735 is 3.

• What are the factors of 735?

  Factors of 735 are 1 , 3 , 5 , 7 , 15 , 21 , 35 , 49 , 105 , 147 , 245 , 735.

• What is prime factorization of 735 in exponential form?

  Prime factorization of 735 in exponential form is 3 x 5 x 7².

• Is 735 a prime number or a composite number?

  735 is a composite number.

• Is 735 a prime number?

  false, 735 is not a prime number.

• What is the sum of all prime factors of 735?

  Prime factors of 735 are 3 x 5 x 7 x 7. Therefore, their sum is 22.

• What is the product of all prime factors of 735?

  Prime factors of 735 are 3 x 5 x 7 x 7. Therefore, their product is 735.

• What numbers are the prime factors of 735?

  Prime factors of 735 are 3 , 5 , 7 , 7.

• What is the sum of all odd prime factors of 735?

  Prime factors of 735 are 3 , 5 , 7 , 7, out of which 3 , 5 , 7 , 7 are odd numbers. So, the sum of odd prime factors of 735 is 3 + 5 + 7 + 7 = 22.