# Prime Factors of 1023

Prime Factors of 1023 are 3, 11, and 31

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

 1.   Prime Factorization of 1023 by Division Method 2.   Prime Factorization of 1023 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 1023 by Division Method

To find the primefactors of 1023 using the division method, follow these steps:

• Step 1. Start dividing 1023 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 1023, which is 3. Divide 1023 by 3 to obtain the quotient (341).
1023 ÷ 3 = 341
• Step 3. Repeat step 1 with the obtained quotient (341).
341 ÷ 11 = 31
31 ÷ 31 = 1

So, the prime factorization of 1023 is, 1023 = 3 x 11 x 31.

#### Steps to find Prime Factors of 1023 by Factor Tree Method

We can follow the same procedure using the factor tree of 1023 as shown below:

So, the prime factorization of 1023 is, 1023 = 3 x 11 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 1023 are 3 x 11 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 1023 but not a prime factor of 1023.

• Which is the smallest prime factor of 1023?

Smallest prime factor of 1023 is 3.

• What are the factors of 1023?

Factors of 1023 are 1 , 3 , 11 , 31 , 33 , 93 , 341 , 1023.

• What is prime factorization of 1023 in exponential form?

Prime factorization of 1023 in exponential form is 3 x 11 x 31.

• Is 1023 a prime number or a composite number?

1023 is a composite number.

• Is 1023 a prime number?

false, 1023 is not a prime number.

• What is the sum of all prime factors of 1023?

Prime factors of 1023 are 3 x 11 x 31. Therefore, their sum is 45.

• What is the product of all prime factors of 1023?

Prime factors of 1023 are 3 x 11 x 31. Therefore, their product is 1023.

• What numbers are the prime factors of 1023?

Prime factors of 1023 are 3 , 11 , 31.

• What is the sum of all odd prime factors of 1023?

Prime factors of 1023 are 3 , 11 , 31, out of which 3 , 11 , 31 are odd numbers. So, the sum of odd prime factors of 1023 is 3 + 11 + 31 = 45.