# Prime Factors of 343

Prime Factors of 343 are 7, 7, and 7

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

 1.   Prime Factorization of 343 by Division Method 2.   Prime Factorization of 343 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 343 by Division Method

To find the primefactors of 343 using the division method, follow these steps:

• Step 1. Start dividing 343 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 343, which is 7. Divide 343 by 7 to obtain the quotient (49).
343 ÷ 7 = 49
• Step 3. Repeat step 1 with the obtained quotient (49).
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 343 is, 343 = 7 x 7 x 7.

#### Steps to find Prime Factors of 343 by Factor Tree Method

We can follow the same procedure using the factor tree of 343 as shown below:

So, the prime factorization of 343 is, 343 = 7 x 7 x 7.

#### 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 343 are 7 x 7 x 7.

#### 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 343 but not a prime factor of 343.

• Which is the smallest prime factor of 343?

Smallest prime factor of 343 is 7.

• What are the factors of 343?

Factors of 343 are 1 , 7 , 49 , 343.

• What is prime factorization of 343 in exponential form?

Prime factorization of 343 in exponential form is 73.

• Is 343 a prime number or a composite number?

343 is a composite number.

• Is 343 a prime number?

false, 343 is not a prime number.

• What is the sum of all prime factors of 343?

Prime factors of 343 are 7 x 7 x 7. Therefore, their sum is 21.

• What is the product of all prime factors of 343?

Prime factors of 343 are 7 x 7 x 7. Therefore, their product is 343.

• What numbers are the prime factors of 343?

Prime factors of 343 are 7 , 7 , 7.

• What is the sum of all odd prime factors of 343?

Prime factors of 343 are 7 , 7 , 7, out of which 7 , 7 , 7 are odd numbers. So, the sum of odd prime factors of 343 is 7 + 7 + 7 = 21.