# Prime Factors of 822

Prime Factors of 822 are 2, 3, and 137

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

 1.   Prime Factorization of 822 by Division Method 2.   Prime Factorization of 822 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 822 by Division Method

To find the primefactors of 822 using the division method, follow these steps:

• Step 1. Start dividing 822 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 822, which is 2. Divide 822 by 2 to obtain the quotient (411).
822 ÷ 2 = 411
• Step 3. Repeat step 1 with the obtained quotient (411).
411 ÷ 3 = 137
137 ÷ 137 = 1

So, the prime factorization of 822 is, 822 = 2 x 3 x 137.

#### Steps to find Prime Factors of 822 by Factor Tree Method

We can follow the same procedure using the factor tree of 822 as shown below:

So, the prime factorization of 822 is, 822 = 2 x 3 x 137.

#### 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 822 are 2 x 3 x 137.

#### 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 822 but not a prime factor of 822.

#### Frequently Asked Questions

• Which is the smallest prime factor of 822?

Smallest prime factor of 822 is 2.

• Is 822 a perfect square?

No 822 is not a perfect square.

• What is the prime factorization of 822?

Prime factorization of 822 is 2 x 3 x 137.

• What are the factors of 822?

Factors of 822 are 1 , 2 , 3 , 6 , 137 , 274 , 411 , 822.

• What is the product of all prime factors of 822?

Prime factors of 822 are 2 x 3 x 137. Therefore, their product is 822.

• What numbers are the prime factors of 822?

Prime factors of 822 are 2 , 3 , 137.

• What is the sum of all odd prime factors of 822?

Prime factors of 822 are 2 , 3 , 137, out of which 3 , 137 are odd numbers. So, the sum of odd prime factors of 822 is 3 + 137 = 140.

• Is there any even prime factor of 822?

Yes there is a even prime factor of 822.

• What is the product of all odd prime factors of 822?

Prime factors of 822 are 2 , 3 , 137, out of which 3 , 137 are odd numbers. So, the product of odd prime factors of 822 is 3 x 137 = 411.

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