Prime Factors of 4004

Steps to find Prime Factors of 4004 by Division Method

To find the primefactors of 4004 using the division method, follow these steps:

• Step 1. Start dividing 4004 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 4004, which is 2. Divide 4004 by 2 to obtain the quotient (2002).
  4004 ÷ 2 = 2002
• Step 3. Repeat step 1 with the obtained quotient (2002).
  2002 ÷ 2 = 1001
  1001 ÷ 7 = 143
  143 ÷ 11 = 13
  13 ÷ 13 = 1

So, the prime factorization of 4004 is, 4004 = 2 x 2 x 7 x 11 x 13.

Steps to find Prime Factors of 4004 by Factor Tree Method

We can follow the same procedure using the factor tree of 4004 as shown below:

So, the prime factorization of 4004 is, 4004 = 2 x 2 x 7 x 11 x 13.

What does Prime factor of a number mean?

A prime number in mathematics is defined as any natural number greater than 1, that is not divisible by any number except 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 4004 are 2 x 2 x 7 x 11 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 4004 but not a prime factor of 4004.

Frequently Asked Questions

• Which is the smallest prime factor of 4004?

  Smallest prime factor of 4004 is 2.

• What is the prime factorization of 4004?

  Prime factorization of 4004 is 2 x 2 x 7 x 11 x 13.

• What are the factors of 4004?

  Factors of 4004 are 1 , 2 , 4 , 7 , 11 , 13 , 14 , 22 , 26 , 28 , 44 , 52 , 77 , 91 , 143 , 154 , 182 , 286 , 308 , 364 , 572 , 1001 , 2002 , 4004.

• Is 4004 a prime number or a composite number?

  4004 is a composite number.

• Is 4004 a prime number?

  false, 4004 is not a prime number.

• Which is the largest prime factors of 4004?

  The largest prime factor of 4004 is 13.

• What is the sum of all prime factors of 4004?

  Prime factors of 4004 are 2 x 2 x 7 x 11 x 13. Therefore, their sum is 35.

• What numbers are the prime factors of 4004?

  Prime factors of 4004 are 2 , 2 , 7 , 11 , 13.

• What is the sum of all odd prime factors of 4004?

  Prime factors of 4004 are 2 , 2 , 7 , 11 , 13, out of which 7 , 11 , 13 are odd numbers. So, the sum of odd prime factors of 4004 is 7 + 11 + 13 = 31.