Prime Factors of 2007

Steps to find Prime Factors of 2007 by Division Method

To find the primefactors of 2007 using the division method, follow these steps:

• Step 1. Start dividing 2007 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 2007, which is 3. Divide 2007 by 3 to obtain the quotient (669).
  2007 ÷ 3 = 669
• Step 3. Repeat step 1 with the obtained quotient (669).
  669 ÷ 3 = 223
  223 ÷ 223 = 1

So, the prime factorization of 2007 is, 2007 = 3 x 3 x 223.

Steps to find Prime Factors of 2007 by Factor Tree Method

We can follow the same procedure using the factor tree of 2007 as shown below:

So, the prime factorization of 2007 is, 2007 = 3 x 3 x 223.

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 2007 are 3 x 3 x 223.

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 2007 but not a prime factor of 2007.

Frequently Asked Questions

• Which is the smallest prime factor of 2007?

  Smallest prime factor of 2007 is 3.

• What are the factors of 2007?

  Factors of 2007 are 1 , 3 , 9 , 223 , 669 , 2007.

• What is prime factorization of 2007 in exponential form?

  Prime factorization of 2007 in exponential form is 3² x 223.

• Is 2007 a prime number or a composite number?

  2007 is a composite number.

• Is 2007 a prime number?

  false, 2007 is not a prime number.

• What is the sum of all prime factors of 2007?

  Prime factors of 2007 are 3 x 3 x 223. Therefore, their sum is 229.

• What is the product of all prime factors of 2007?

  Prime factors of 2007 are 3 x 3 x 223. Therefore, their product is 2007.

• What numbers are the prime factors of 2007?

  Prime factors of 2007 are 3 , 3 , 223.

• What is the sum of all odd prime factors of 2007?

  Prime factors of 2007 are 3 , 3 , 223, out of which 3 , 3 , 223 are odd numbers. So, the sum of odd prime factors of 2007 is 3 + 3 + 223 = 229.