Prime Factors of 7875

Steps to find Prime Factors of 7875 by Division Method

To find the primefactors of 7875 using the division method, follow these steps:

• Step 1. Start dividing 7875 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 7875, which is 3. Divide 7875 by 3 to obtain the quotient (2625).
  7875 ÷ 3 = 2625
• Step 3. Repeat step 1 with the obtained quotient (2625).
  2625 ÷ 3 = 875
  875 ÷ 5 = 175
  175 ÷ 5 = 35
  35 ÷ 5 = 7
  7 ÷ 7 = 1

So, the prime factorization of 7875 is, 7875 = 3 x 3 x 5 x 5 x 5 x 7.

Steps to find Prime Factors of 7875 by Factor Tree Method

We can follow the same procedure using the factor tree of 7875 as shown below:

So, the prime factorization of 7875 is, 7875 = 3 x 3 x 5 x 5 x 5 x 7.

Definition of Prime Factors?

In mathematics, prime numbers are defined as all those whole numbers greater than 1 that have only two factors, i.e. 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 7875 are 3 x 3 x 5 x 5 x 5 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 7875 but not a prime factor of 7875.

Frequently Asked Questions

• Which is the smallest prime factor of 7875?

  Smallest prime factor of 7875 is 3.

• Is 7875 a perfect square?

  No 7875 is not a perfect square.

• What is the prime factorization of 7875?

  Prime factorization of 7875 is 3 x 3 x 5 x 5 x 5 x 7.

• What is prime factorization of 7875 in exponential form?

  Prime factorization of 7875 in exponential form is 3² x 5³ x 7.

• Is 7875 a prime number?

  false, 7875 is not a prime number.

• Which is the largest prime factors of 7875?

  The largest prime factor of 7875 is 7.

• What is the product of all prime factors of 7875?

  Prime factors of 7875 are 3 x 3 x 5 x 5 x 5 x 7. Therefore, their product is 7875.

• What is the sum of all odd prime factors of 7875?

  Prime factors of 7875 are 3 , 3 , 5 , 5 , 5 , 7, out of which 3 , 3 , 5 , 5 , 5 , 7 are odd numbers. So, the sum of odd prime factors of 7875 is 3 + 3 + 5 + 5 + 5 + 7 = 28.

• What is the product of all odd prime factors of 7875?

  Prime factors of 7875 are 3 , 3 , 5 , 5 , 5 , 7, out of which 3 , 3 , 5 , 5 , 5 , 7 are odd numbers. So, the product of odd prime factors of 7875 is 3 x 3 x 5 x 5 x 5 x 7 = 7875.