Prime Factors of 259

Steps to find Prime Factors of 259 by Division Method

To find the primefactors of 259 using the division method, follow these steps:

• Step 1. Start dividing 259 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 259, which is 7. Divide 259 by 7 to obtain the quotient (37).
  259 ÷ 7 = 37
• Step 3. Repeat step 1 with the obtained quotient (37).
  37 ÷ 37 = 1

So, the prime factorization of 259 is, 259 = 7 x 37.

Steps to find Prime Factors of 259 by Factor Tree Method

We can follow the same procedure using the factor tree of 259 as shown below:

So, the prime factorization of 259 is, 259 = 7 x 37.

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 259 are 7 x 37.

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 259 but not a prime factor of 259.

Frequently Asked Questions

• Which is the smallest prime factor of 259?

  Smallest prime factor of 259 is 7.

• Is 259 a perfect square?

  No 259 is not a perfect square.

• What is the prime factorization of 259?

  Prime factorization of 259 is 7 x 37.

• What is prime factorization of 259 in exponential form?

  Prime factorization of 259 in exponential form is 7 x 37.

• Is 259 a prime number?

  false, 259 is not a prime number.

• Which is the largest prime factors of 259?

  The largest prime factor of 259 is 37.

• What is the product of all prime factors of 259?

  Prime factors of 259 are 7 x 37. Therefore, their product is 259.

• What is the sum of all odd prime factors of 259?

  Prime factors of 259 are 7 , 37, out of which 7 , 37 are odd numbers. So, the sum of odd prime factors of 259 is 7 + 37 = 44.

• What is the product of all odd prime factors of 259?

  Prime factors of 259 are 7 , 37, out of which 7 , 37 are odd numbers. So, the product of odd prime factors of 259 is 7 x 37 = 259.