Prime Factors of 723

Steps to find Prime Factors of 723 by Division Method

To find the primefactors of 723 using the division method, follow these steps:

• Step 1. Start dividing 723 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 723, which is 3. Divide 723 by 3 to obtain the quotient (241).
  723 ÷ 3 = 241
• Step 3. Repeat step 1 with the obtained quotient (241).
  241 ÷ 241 = 1

So, the prime factorization of 723 is, 723 = 3 x 241.

Steps to find Prime Factors of 723 by Factor Tree Method

We can follow the same procedure using the factor tree of 723 as shown below:

So, the prime factorization of 723 is, 723 = 3 x 241.

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 723 are 3 x 241.

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 723 but not a prime factor of 723.

Frequently Asked Questions

• Which is the smallest prime factor of 723?

  Smallest prime factor of 723 is 3.

• Is 723 a perfect square?

  No 723 is not a perfect square.

• What is the prime factorization of 723?

  Prime factorization of 723 is 3 x 241.

• What is prime factorization of 723 in exponential form?

  Prime factorization of 723 in exponential form is 3 x 241.

• Is 723 a prime number?

  false, 723 is not a prime number.

• Which is the largest prime factors of 723?

  The largest prime factor of 723 is 241.

• What is the product of all prime factors of 723?

  Prime factors of 723 are 3 x 241. Therefore, their product is 723.

• What is the sum of all odd prime factors of 723?

  Prime factors of 723 are 3 , 241, out of which 3 , 241 are odd numbers. So, the sum of odd prime factors of 723 is 3 + 241 = 244.

• What is the product of all odd prime factors of 723?

  Prime factors of 723 are 3 , 241, out of which 3 , 241 are odd numbers. So, the product of odd prime factors of 723 is 3 x 241 = 723.