Prime Factors of 728

Steps to find Prime Factors of 728 by Division Method

To find the primefactors of 728 using the division method, follow these steps:

• Step 1. Start dividing 728 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 728, which is 2. Divide 728 by 2 to obtain the quotient (364).
  728 ÷ 2 = 364
• Step 3. Repeat step 1 with the obtained quotient (364).
  364 ÷ 2 = 182
  182 ÷ 2 = 91
  91 ÷ 7 = 13
  13 ÷ 13 = 1

So, the prime factorization of 728 is, 728 = 2 x 2 x 2 x 7 x 13.

Steps to find Prime Factors of 728 by Factor Tree Method

We can follow the same procedure using the factor tree of 728 as shown below:

So, the prime factorization of 728 is, 728 = 2 x 2 x 2 x 7 x 13.

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 728 are 2 x 2 x 2 x 7 x 13.

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 728 but not a prime factor of 728.

Frequently Asked Questions

• Which is the smallest prime factor of 728?

  Smallest prime factor of 728 is 2.

• Is 728 a perfect square?

  No 728 is not a perfect square.

• What is the prime factorization of 728?

  Prime factorization of 728 is 2 x 2 x 2 x 7 x 13.

• What is prime factorization of 728 in exponential form?

  Prime factorization of 728 in exponential form is 2³ x 7 x 13.

• Is 728 a prime number or a composite number?

  728 is a composite number.

• Which is the largest prime factors of 728?

  The largest prime factor of 728 is 13.

• What is the product of all prime factors of 728?

  Prime factors of 728 are 2 x 2 x 2 x 7 x 13. Therefore, their product is 728.

• What numbers are the prime factors of 728?

  Prime factors of 728 are 2 , 2 , 2 , 7 , 13.

• Is there any even prime factor of 728?

  Yes there is a even prime factor of 728.