Prime Factors of 75

Steps to find Prime Factors of 75 by Division Method

To find the primefactors of 75 using the division method, follow these steps:

• Step 1. Start dividing 75 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 75, which is 3. Divide 75 by 3 to obtain the quotient (25).
  75 ÷ 3 = 25
• Step 3. Repeat step 1 with the obtained quotient (25).
  25 ÷ 5 = 5
  5 ÷ 5 = 1

So, the prime factorization of 75 is, 75 = 3 x 5 x 5.

Steps to find Prime Factors of 75 by Factor Tree Method

We can follow the same procedure using the factor tree of 75 as shown below:

So, the prime factorization of 75 is, 75 = 3 x 5 x 5.

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 75 are 3 x 5 x 5.

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 75 but not a prime factor of 75.

Frequently Asked Questions

• Which is the smallest prime factor of 75?

  Smallest prime factor of 75 is 3.

• Is 75 a perfect square?

  No 75 is not a perfect square.

• What is the prime factorization of 75?

  Prime factorization of 75 is 3 x 5 x 5.

• What is prime factorization of 75 in exponential form?

  Prime factorization of 75 in exponential form is 3 x 5².

• Is 75 a prime number?

  false, 75 is not a prime number.

• Which is the largest prime factors of 75?

  The largest prime factor of 75 is 5.

• What is the product of all prime factors of 75?

  Prime factors of 75 are 3 x 5 x 5. Therefore, their product is 75.

• What is the sum of all odd prime factors of 75?

  Prime factors of 75 are 3 , 5 , 5, out of which 3 , 5 , 5 are odd numbers. So, the sum of odd prime factors of 75 is 3 + 5 + 5 = 13.

• What is the product of all odd prime factors of 75?

  Prime factors of 75 are 3 , 5 , 5, out of which 3 , 5 , 5 are odd numbers. So, the product of odd prime factors of 75 is 3 x 5 x 5 = 75.