# Prime Factors of 59319

Prime Factors of 59319 are 3, 3, 3, 13, 13, and 13

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

 1.   Prime Factorization of 59319 by Division Method 2.   Prime Factorization of 59319 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 59319 by Division Method

To find the primefactors of 59319 using the division method, follow these steps:

• Step 1. Start dividing 59319 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 59319, which is 3. Divide 59319 by 3 to obtain the quotient (19773).
59319 ÷ 3 = 19773
• Step 3. Repeat step 1 with the obtained quotient (19773).
19773 ÷ 3 = 6591
6591 ÷ 3 = 2197
2197 ÷ 13 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1

So, the prime factorization of 59319 is, 59319 = 3 x 3 x 3 x 13 x 13 x 13.

#### Steps to find Prime Factors of 59319 by Factor Tree Method

We can follow the same procedure using the factor tree of 59319 as shown below:

So, the prime factorization of 59319 is, 59319 = 3 x 3 x 3 x 13 x 13 x 13.

#### What does Prime factor of a number mean?

A prime number in mathematics is defined as any natural number greater than 1, that is not divisible by any number except 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 59319 are 3 x 3 x 3 x 13 x 13 x 13.

#### 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 59319 but not a prime factor of 59319.

• Which is the smallest prime factor of 59319?

Smallest prime factor of 59319 is 3.

• What are the factors of 59319?

Factors of 59319 are 1 , 3 , 9 , 13 , 27 , 39 , 117 , 169 , 351 , 507 , 1521 , 2197 , 4563 , 6591 , 19773 , 59319.

• What is prime factorization of 59319 in exponential form?

Prime factorization of 59319 in exponential form is 33 x 133.

• Is 59319 a prime number or a composite number?

59319 is a composite number.

• Is 59319 a prime number?

false, 59319 is not a prime number.

• What is the sum of all prime factors of 59319?

Prime factors of 59319 are 3 x 3 x 3 x 13 x 13 x 13. Therefore, their sum is 48.

• What is the product of all prime factors of 59319?

Prime factors of 59319 are 3 x 3 x 3 x 13 x 13 x 13. Therefore, their product is 59319.

• What numbers are the prime factors of 59319?

Prime factors of 59319 are 3 , 3 , 3 , 13 , 13 , 13.

• What is the sum of all odd prime factors of 59319?

Prime factors of 59319 are 3 , 3 , 3 , 13 , 13 , 13, out of which 3 , 3 , 3 , 13 , 13 , 13 are odd numbers. So, the sum of odd prime factors of 59319 is 3 + 3 + 3 + 13 + 13 + 13 = 48.