Prime Factors of 667

Steps to find Prime Factors of 667 by Division Method

To find the primefactors of 667 using the division method, follow these steps:

• Step 1. Start dividing 667 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 667, which is 23. Divide 667 by 23 to obtain the quotient (29).
  667 ÷ 23 = 29
• Step 3. Repeat step 1 with the obtained quotient (29).
  29 ÷ 29 = 1

So, the prime factorization of 667 is, 667 = 23 x 29.

Steps to find Prime Factors of 667 by Factor Tree Method

We can follow the same procedure using the factor tree of 667 as shown below:

So, the prime factorization of 667 is, 667 = 23 x 29.

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 667 are 23 x 29.

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 667 but not a prime factor of 667.

Frequently Asked Questions

• Which is the smallest prime factor of 667?

  Smallest prime factor of 667 is 23.

• Is 667 a perfect square?

  No 667 is not a perfect square.

• What is the prime factorization of 667?

  Prime factorization of 667 is 23 x 29.

• What is prime factorization of 667 in exponential form?

  Prime factorization of 667 in exponential form is 23 x 29.

• Is 667 a prime number?

  false, 667 is not a prime number.

• Which is the largest prime factors of 667?

  The largest prime factor of 667 is 29.

• What is the product of all prime factors of 667?

  Prime factors of 667 are 23 x 29. Therefore, their product is 667.

• What is the sum of all odd prime factors of 667?

  Prime factors of 667 are 23 , 29, out of which 23 , 29 are odd numbers. So, the sum of odd prime factors of 667 is 23 + 29 = 52.

• What is the product of all odd prime factors of 667?

  Prime factors of 667 are 23 , 29, out of which 23 , 29 are odd numbers. So, the product of odd prime factors of 667 is 23 x 29 = 667.