Prime Factors of 657

Steps to find Prime Factors of 657 by Division Method

To find the primefactors of 657 using the division method, follow these steps:

• Step 1. Start dividing 657 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 657, which is 3. Divide 657 by 3 to obtain the quotient (219).
  657 ÷ 3 = 219
• Step 3. Repeat step 1 with the obtained quotient (219).
  219 ÷ 3 = 73
  73 ÷ 73 = 1

So, the prime factorization of 657 is, 657 = 3 x 3 x 73.

Steps to find Prime Factors of 657 by Factor Tree Method

We can follow the same procedure using the factor tree of 657 as shown below:

So, the prime factorization of 657 is, 657 = 3 x 3 x 73.

How do you define Prime Factors of a number?

Prime numbers, in mathematics are all those natural numbers greater than 1 that have exactly 2 factors which are 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 657 are 3 x 3 x 73.

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 657 but not a prime factor of 657.

Frequently Asked Questions

• Which is the smallest prime factor of 657?

  Smallest prime factor of 657 is 3.

• What is the prime factorization of 657?

  Prime factorization of 657 is 3 x 3 x 73.

• What is prime factorization of 657 in exponential form?

  Prime factorization of 657 in exponential form is 3² x 73.

• Is 657 a prime number or a composite number?

  657 is a composite number.

• Is 657 a prime number?

  false, 657 is not a prime number.

• How to find prime factorization of 657 easily?

  To find prime factorization of 657 easily you can refer to the steps given on this page step by step.

• Which is the largest prime factors of 657?

  The largest prime factor of 657 is 73.

• What is the product of all prime factors of 657?

  Prime factors of 657 are 3 x 3 x 73. Therefore, their product is 657.

• What is the sum of all odd prime factors of 657?

  Prime factors of 657 are 3 , 3 , 73, out of which 3 , 3 , 73 are odd numbers. So, the sum of odd prime factors of 657 is 3 + 3 + 73 = 79.