# Prime Factors of 403

Prime Factors of 403 are 13 and 31

#### How to find prime factors of a number

 1.   Prime Factorization of 403 by Division Method 2.   Prime Factorization of 403 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 403 by Division Method

To find the primefactors of 403 using the division method, follow these steps:

• Step 1. Start dividing 403 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 403, which is 13. Divide 403 by 13 to obtain the quotient (31).
403 ÷ 13 = 31
• Step 3. Repeat step 1 with the obtained quotient (31).
31 ÷ 31 = 1

So, the prime factorization of 403 is, 403 = 13 x 31.

#### Steps to find Prime Factors of 403 by Factor Tree Method

We can follow the same procedure using the factor tree of 403 as shown below:

So, the prime factorization of 403 is, 403 = 13 x 31.

#### 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 403 are 13 x 31.

#### 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 403 but not a prime factor of 403.

• Which is the smallest prime factor of 403?

Smallest prime factor of 403 is 13.

• Is 403 a perfect square?

No 403 is not a perfect square.

• What is the prime factorization of 403?

Prime factorization of 403 is 13 x 31.

• What is prime factorization of 403 in exponential form?

Prime factorization of 403 in exponential form is 13 x 31.

• Is 403 a prime number?

false, 403 is not a prime number.

• Which is the largest prime factors of 403?

The largest prime factor of 403 is 31.

• What is the product of all prime factors of 403?

Prime factors of 403 are 13 x 31. Therefore, their product is 403.

• What is the sum of all odd prime factors of 403?

Prime factors of 403 are 13 , 31, out of which 13 , 31 are odd numbers. So, the sum of odd prime factors of 403 is 13 + 31 = 44.

• What is the product of all odd prime factors of 403?

Prime factors of 403 are 13 , 31, out of which 13 , 31 are odd numbers. So, the product of odd prime factors of 403 is 13 x 31 = 403.