# Prime Factors of 782

Prime Factors of 782 are 2, 17, and 23

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

 1.   Prime Factorization of 782 by Division Method 2.   Prime Factorization of 782 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 782 by Division Method

To find the primefactors of 782 using the division method, follow these steps:

• Step 1. Start dividing 782 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 782, which is 2. Divide 782 by 2 to obtain the quotient (391).
782 ÷ 2 = 391
• Step 3. Repeat step 1 with the obtained quotient (391).
391 ÷ 17 = 23
23 ÷ 23 = 1

So, the prime factorization of 782 is, 782 = 2 x 17 x 23.

#### Steps to find Prime Factors of 782 by Factor Tree Method

We can follow the same procedure using the factor tree of 782 as shown below:

So, the prime factorization of 782 is, 782 = 2 x 17 x 23.

#### 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 782 are 2 x 17 x 23.

#### Properties of Prime Factors

• Two prime factors of a given number are always coprime to each other.
• 2 is the only even prime factor any number can have.
• Two prime factors 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 782 but not a prime factor of 782.

• Which is the smallest prime factor of 782?

Smallest prime factor of 782 is 2.

• Is 782 a perfect square?

No 782 is not a perfect square.

• What is the prime factorization of 782?

Prime factorization of 782 is 2 x 17 x 23.

• What are the factors of 782?

Factors of 782 are 1 , 2 , 17 , 23 , 34 , 46 , 391 , 782.

• What is the product of all prime factors of 782?

Prime factors of 782 are 2 x 17 x 23. Therefore, their product is 782.

• What numbers are the prime factors of 782?

Prime factors of 782 are 2 , 17 , 23.

• What is the sum of all odd prime factors of 782?

Prime factors of 782 are 2 , 17 , 23, out of which 17 , 23 are odd numbers. So, the sum of odd prime factors of 782 is 17 + 23 = 40.

• Is there any even prime factor of 782?

Yes there is a even prime factor of 782.

• What is the product of all odd prime factors of 782?

Prime factors of 782 are 2 , 17 , 23, out of which 17 , 23 are odd numbers. So, the product of odd prime factors of 782 is 17 x 23 = 391.