Prime Factors of 975

Steps to find Prime Factors of 975 by Division Method

To find the primefactors of 975 using the division method, follow these steps:

• Step 1. Start dividing 975 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 975, which is 3. Divide 975 by 3 to obtain the quotient (325).
  975 ÷ 3 = 325
• Step 3. Repeat step 1 with the obtained quotient (325).
  325 ÷ 5 = 65
  65 ÷ 5 = 13
  13 ÷ 13 = 1

So, the prime factorization of 975 is, 975 = 3 x 5 x 5 x 13.

Steps to find Prime Factors of 975 by Factor Tree Method

We can follow the same procedure using the factor tree of 975 as shown below:

So, the prime factorization of 975 is, 975 = 3 x 5 x 5 x 13.

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 975 are 3 x 5 x 5 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 975 but not a prime factor of 975.

Frequently Asked Questions

• Which is the smallest prime factor of 975?

  Smallest prime factor of 975 is 3.

• What are the factors of 975?

  Factors of 975 are 1 , 3 , 5 , 13 , 15 , 25 , 39 , 65 , 75 , 195 , 325 , 975.

• What is prime factorization of 975 in exponential form?

  Prime factorization of 975 in exponential form is 3 x 5² x 13.

• Is 975 a prime number or a composite number?

  975 is a composite number.

• Is 975 a prime number?

  false, 975 is not a prime number.

• What is the sum of all prime factors of 975?

  Prime factors of 975 are 3 x 5 x 5 x 13. Therefore, their sum is 26.

• What is the product of all prime factors of 975?

  Prime factors of 975 are 3 x 5 x 5 x 13. Therefore, their product is 975.

• What numbers are the prime factors of 975?

  Prime factors of 975 are 3 , 5 , 5 , 13.

• What is the sum of all odd prime factors of 975?

  Prime factors of 975 are 3 , 5 , 5 , 13, out of which 3 , 5 , 5 , 13 are odd numbers. So, the sum of odd prime factors of 975 is 3 + 5 + 5 + 13 = 26.