Prime Factors of 1251

Steps to find Prime Factors of 1251 by Division Method

To find the primefactors of 1251 using the division method, follow these steps:

• Step 1. Start dividing 1251 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 1251, which is 3. Divide 1251 by 3 to obtain the quotient (417).
  1251 ÷ 3 = 417
• Step 3. Repeat step 1 with the obtained quotient (417).
  417 ÷ 3 = 139
  139 ÷ 139 = 1

So, the prime factorization of 1251 is, 1251 = 3 x 3 x 139.

Steps to find Prime Factors of 1251 by Factor Tree Method

We can follow the same procedure using the factor tree of 1251 as shown below:

So, the prime factorization of 1251 is, 1251 = 3 x 3 x 139.

Introduction to Prime Factors?

In mathematics, prime numbers are defined as all those natural numbers greater than 1 that has only two divisors one being number 1 and the other being the number itself. When we express any number as the products of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 1251 are 3 x 3 x 139.

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 1251 but not a prime factor of 1251.

Frequently Asked Questions

• Which is the smallest prime factor of 1251?

  Smallest prime factor of 1251 is 3.

• Is 1251 a perfect square?

  No 1251 is not a perfect square.

• What is the prime factorization of 1251?

  Prime factorization of 1251 is 3 x 3 x 139.

• What is prime factorization of 1251 in exponential form?

  Prime factorization of 1251 in exponential form is 3² x 139.

• Is 1251 a prime number?

  false, 1251 is not a prime number.

• Which is the largest prime factors of 1251?

  The largest prime factor of 1251 is 139.

• What is the product of all prime factors of 1251?

  Prime factors of 1251 are 3 x 3 x 139. Therefore, their product is 1251.

• What is the sum of all odd prime factors of 1251?

  Prime factors of 1251 are 3 , 3 , 139, out of which 3 , 3 , 139 are odd numbers. So, the sum of odd prime factors of 1251 is 3 + 3 + 139 = 145.

• What is the product of all odd prime factors of 1251?

  Prime factors of 1251 are 3 , 3 , 139, out of which 3 , 3 , 139 are odd numbers. So, the product of odd prime factors of 1251 is 3 x 3 x 139 = 1251.